Instruction

1

If the baseline

**degree**given in the format of fractions, the transaction must be made in two steps. The sequence for the results no impact - start, for example, extract from the root of the degree indicated in the denominator of the fraction. For example, to build in**the degree**⅔ , the number 64 in this step, it is necessary to extract the cube root of 64^ ⅔ = (3√64)2 = 42.2

Lift obtained in the first step the value in

**a degree**equal to the number standing in the numerator of the fraction. The result of this operation will be the result of a number raised to a fractional**degree**. For example, from the previous step is fully described, the calculations can be written as: 64^ ⅔ = (3√64)2 = 42 = 16.3

Based on the ease of calculation when determining the sequence of the above-described operations of root extraction and raising to

**a degree**. For example, if required to the same**degree**⅔ to build the number 8, starting with the extraction of the cube root of eight would be impractical because the result would be a fractional number. In this case it is better to start with the construction of 8 square and then remove the root of the third degree 64 and thus to dispense with the fractional intermediate values: 8^ ⅔ = 3√(82) = 3√64 = 4.4

If the exponent in the original data is given in decimal fractions, we start with converting it to an ordinary fraction, and then proceed according to the above algorithm. For example, to raise a number to

**a degree**of 0.75 transform this figure into an ordinary fraction¾, then extract the fourth root, and construct the result.5

Use any calculator if the calculations are not important, important is only the result. This can be a script embedded in Google's search engine is to use it to find the value you want is even easier than using a standard calculator Windows. For example, raising the number to 15

**degree**⅗ go to the home page and type in the search query box 15^(3/5). The result of the calculation with a precision of up to 8 characters Google will display even without clicking the button send request: 15^(3 / 5) = 5,07755639.# Advice 2: How to calculate power of number

**apart in school algebra lessons. In life, this operation is rarely performed. For example, when calculating the area of a square or volume of a cube is used because the length, width, and the cube, and height – equal values. Otherwise, exponentiation is most likely to be applied during the production.**

**The degree***numbers*You will need

- Paper, pen, scientific calculator, table of degrees, software (e.g., spreadsheet Excel).

Instruction

1

To calculate the degree

For this, the number X multiplied by itself n times.

*number*in mathematical language means to build any number to any degree. Suppose you want the number X raised to the power n.For this, the number X multiplied by itself n times.

2

Let X = 125, and the degree

125^3 = 125*125*125 = 1 953 125

Another example.

3^4 = 3*3*3*3 = 81

*of number*, i.e. n = 3. This means that the number 125 you need to multiply on itself 3 times.125^3 = 125*125*125 = 1 953 125

Another example.

3^4 = 3*3*3*3 = 81

3

When working with a negative number you need to be careful with the signs. It should be remembered that even the degree (n) yields a plus sign, odd – minus sign.

For example

(-7)^2 = (-7)*(-7) = 49

(-7)^3 = (-7)*(-7)*(-7) = 343

For example

(-7)^2 = (-7)*(-7) = 49

(-7)^3 = (-7)*(-7)*(-7) = 343

4

Zero degree (n = 0) from any

15^0 = 1

(-6)^0 = 1

(1/3)^0 = 1if n = 1, the number to multiply with itself is not necessary.

Will

7^1 = 7

329^1 = 329

*number*will always be equal to one.15^0 = 1

(-6)^0 = 1

(1/3)^0 = 1if n = 1, the number to multiply with itself is not necessary.

Will

7^1 = 7

329^1 = 329

5

The opposite of the construction of a

If 5^2 = 25, the square root of 25 is 5.

If 5^3 = 125, then the root of the third degree is equal to 5.

If 8^4= 4 096, the fourth root of 4 096 will be equal to 8.

*number*to a power is called the root.If 5^2 = 25, the square root of 25 is 5.

If 5^3 = 125, then the root of the third degree is equal to 5.

If 8^4= 4 096, the fourth root of 4 096 will be equal to 8.

6

If n = 2, then the degree is called square if n = 3, the degree is called a cube. The calculation of square and cube of first ten numbers to produce quite easily. But with the increase

*in the number*erected in degree, and with increasing degree, the computations become time consuming. For such calculation we developed a special table. There are also special engineering and online calculators, software. As a simple software product for operations with degrees, you can use the table editor Excel.# Advice 3: How to calculate root of the third degree

When solving some technical problems may need to calculate

**the root of****the third***degree*. Sometimes this number is also called the cubic root. The root of**the third***degree*from this number calls a number, the cube (the third level) is equal to this. That is, if y is**the root of****the third***degree*in the number x must satisfy the condition: y?=x (x is equal to y cube).You will need

- a calculator or computer

Instruction

1

To calculate

**the root of****the third***degree*, use the calculator. It is desirable that it was not a normal calculator, and the calculator used for engineering calculations. However, even with such a calculator, you will not find a special button to retrieve the root of**the third***degree*. So use the function to raise a number to a power. The root**of the third***degree*corresponds to the power of 1/3 (one third).2

To raise a number to the power 1/3 type on the keyboard of the calculator itself. Then press the "exponentiation". This button, depending on the type of calculator may look like xy (in Superscript). Since most calculators there is no possibility to work with conventional (non-decimal) fractions, instead of the number 1/3 type it the approximate value of 0.33. To obtain greater precision, it is necessary to increase the number of "triples", for example, to get 0,33333333333333. Then, click the "=".

3

To calculate

**the root of****the third***degree*on the computer, use the standard Windows calculator. The procedure is completely similar to that described in the previous paragraph instructions. The only difference is the name of the exponentiation. "Computer," the calculator, it looks like x^y.4

If

**the root of****the third***degree*have to be considered systematically, use the program MS Excel. To calculate**the root of****a third***degree*"Excel", type in any cell " = " sign and then select the "fx" insert function. In the appeared window in the list, Select " select "DEGREE." Click "OK". In the newly appeared window enter the string "Number" value, from which to extract**the root**. In the line "Amount," enter the number "1/3" and click "OK". In the cell the table shows the value of the cubic root of the original number.# Advice 4: How to calculate cube root

In technical calculations and in the solution of many tasks is sometimes required to calculate cubic

**root**, i.e. to find such a number, the cube of which is equal to the original. To calculate the value of the cube root scientific calculator is sufficient. However, even on this calculator there are no special keys to calculate cubic root. But using some simple techniques, you can do without this button.You will need

- scientific calculator or computer

Instruction

1

To calculate the cube root find a number that when raised to a third degree will be equal to this. That is, for example, if x is the original number, and the cubic root of this number, you must run the equation:Y3 = x

2

To find the cube root using the calculator, take a calculator and type on it the original number. Then, click on the exponentiation. Now enter the value of the exponent. In this case, he (theoretically) should be equal to 1/3. But, since the use of fractions, even on difficult engineering calculator, then type the rounded value of the number 1/3, that is: 0,33. Then click on the "=". The indicator of the calculator will appear the value. To get a more accurate value, not collect two triples, and more, for example, 0,333333333333.

3

To calculate the cube root on a computer, open the program "calculator". If no corresponding icon on the desktop, do the following:

- click "start";

- select the menu item "Run";

- enter in the window the string "calc".If that appears on the desktop calculator has the usual form (reminiscent of "accounting calculator"), you can put it into run mode engineer calculations. To do this, select "View" and select "Engineering".Now enter the number from which you want to extract the cube root. Then click on the calculator button "x^y". Next, enter the exponent, for example, of 0.33. For more accurate result, you can type a longer value of the exponent, for example, 0,333333333333. To get an accurate result, enter the exponent "1/3" in parentheses. That is, press the keys "(1/3)".

- click "start";

- select the menu item "Run";

- enter in the window the string "calc".If that appears on the desktop calculator has the usual form (reminiscent of "accounting calculator"), you can put it into run mode engineer calculations. To do this, select "View" and select "Engineering".Now enter the number from which you want to extract the cube root. Then click on the calculator button "x^y". Next, enter the exponent, for example, of 0.33. For more accurate result, you can type a longer value of the exponent, for example, 0,333333333333. To get an accurate result, enter the exponent "1/3" in parentheses. That is, press the keys "(1/3)".

4

The calculation in Excel. Run the program, click "=" and choose "DEGREE". Then enter the number from which you want to remove the root of the third degree. Then, the following line appeared window enter the fraction "1/3" and click "OK".

# Advice 5: How to put a fraction into a square

In the solution of arithmetic and algebraic tasks is sometimes required to build

**a fraction**in**a square**. The easiest way to do it when**the fraction**to a decimal is fairly simple calculator. However, if**the fraction**of the ordinary or combined, in the construction of such number in**the square**may experience some difficulties.You will need

- calculator, computer, Excel.

Instruction

1

To build a decimal

**fraction**in**the square**, take a scientific calculator, type it erected in**the square of****the fraction**, and press the construction in the second degree. On most calculators this button is labeled as "x2". On the standard Windows calculator function calculates the**square**looks like "x^2". For example,**square**a decimal, is equal to 3,14: 3,142 = 9,8596.2

To build in

**the square**of a decimal**fraction**on a normal (accounting) a calculator, multiply this number with itself. By the way, some models of calculators the possibility of raising the number in**the square**even in the absence of a special button. So please check the instruction manual for the specific calculator. Sometimes examples of "tricky" exponentiation is given on the back cover or on the box of the calculator. For example, many calculators for the erection of a number in**a square**is enough to press button "x" and "=".3

For raising to

**the square**fractions (consisting of numerator and denominator), erected in**the square**separately the numerator and denominator of this fraction. That is, use the following rule:(b / h)2 = P2 / Z2, where h is the numerator, b – denominator.Example: (3/4)2 = 32/42 = 9/16.4

If erected in

**the square of****the fraction**– combined (composed of a whole part and fractions), you must bring her to the ordinary mind. That is, apply the following formula:(C h/z)2 = ((u*h+h) / h)2 = (p*z+h)2 / Z2, where C is the integer part of mixed fraction.Example: (3 2/5)2 = ((3*5+2) / 5)2 = (3*5+2)2 / 52 = 172 / 52 = 289/25 = 11 14/25.5

If you build in

**a square**ordinary (not decimal) fractions you have to constantly, use the program MS Excel. To do this, enter in one cell the following formula: =DEGREE(A2;2) where A2 is the cell address which will be entered erected in**the square****a fraction**.To tell the program that input numbers must be treated as an ordinary**fraction**(i.e., not to convert it to decimal form), dial before you**roll**the first digit "0" and "gap". That is, for input, for example, the fraction 2/3, you need to enter: "0 2/3" (and press Enter). While in the entry line displays the decimal representation of fractions introduced. The meaning and representation of fractions directly in the cell preserved in its original form. In addition, when using mathematical functions, whose arguments are fractions the result will also be presented in the form of fractions. Hence**the square**of the fraction 2/3 would be represented as 4/9.