Instruction

1

In order to calculate the value of the number having a negative exponent, give the number in the form in which the exponent will become positive value. All numbers with a negative exponent can be represented in the form of an ordinary fraction, the numerator of which is one and the denominator of the original numerical expression with the same degree, just with a plus sign. (see picture).

If we take the example of designation: 3^-5 – three to the minus fifth degree, 3^5, three in the fifth degree, then those tasks will have the form shown in the examples.

Example: 3^-5 = 1 /3^5. Three to the minus fifth power is equal to the fraction: one divided by three in the fifth degree.

If we take the example of designation: 3^-5 – three to the minus fifth degree, 3^5, three in the fifth degree, then those tasks will have the form shown in the examples.

Example: 3^-5 = 1 /3^5. Three to the minus fifth power is equal to the fraction: one divided by three in the fifth degree.

2

Given in fractional form power-law expression is not complicated, but simply converted. To solve it on easy. Raise to a power number, which stands in the denominator. Get the fraction where the numerator, still, is one and the denominator is already raised to the power number.

Example: 3^-5 = 1 /3^5 = 1 / 3 * 3 * 3 * 3 * 3 = 1 / 243. Unit divided by three to the fifth power equal to one divided by two hundred forty-three. In the denominator the number of three erected in the fifth degree, that is, multiplied by itself five times. The result was an ordinary proper fraction.

Example: 3^-5 = 1 /3^5 = 1 / 3 * 3 * 3 * 3 * 3 = 1 / 243. Unit divided by three to the fifth power equal to one divided by two hundred forty-three. In the denominator the number of three erected in the fifth degree, that is, multiplied by itself five times. The result was an ordinary proper fraction.

3

Further, if you are satisfied with the shot, take it, if not, figure on. To do this, divide the numerator by the denominator, that is the unit raised to the power number.

Example: 3^-5 = 1 /3^5 = 1 / 3 * 3 * 3 * 3 * 3 = 1 / 243 = 0,0041. Common fraction equal to a decimal rounded to ten thousandths.

When dividing the numerator by the denominator (to convert fractions to decimal, is often the answer obtained with a large remainder (long value of the fractional part of the answer). In such cases, decided just to round decimals to fractions.

Example: 3^-5 = 1 /3^5 = 1 / 3 * 3 * 3 * 3 * 3 = 1 / 243 = 0,0041. Common fraction equal to a decimal rounded to ten thousandths.

When dividing the numerator by the denominator (to convert fractions to decimal, is often the answer obtained with a large remainder (long value of the fractional part of the answer). In such cases, decided just to round decimals to fractions.

# 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 put in 1 degree

For a brief record of the works of one and the same number by itself, mathematicians have invented the concept of degree. Therefore, the expression 16*16*16*16*16 you can write the shorter way. It would be 16^5. The expression will be read as number 16 in the fifth degree.

You will need

- Paper, pen.

Instruction

1

In General, the

The expression a^n is called

a is the number of base degree,

n is a number, the exponent. For example, a = 4, n = 5,

Then write 4^5 = 4*4*4*4*4 = 1 024

**degree**is written as a^n. This entry means that the number a multiplied by itself n times.The expression a^n is called

**the degree of**u,a is the number of base degree,

n is a number, the exponent. For example, a = 4, n = 5,

Then write 4^5 = 4*4*4*4*4 = 1 024

2

The degree n can be a negative number

n = -1, -2, -3, etc.

To compute the negative

a^(-n) = (1/a)^n = 1/a*1/a*1/a* ... *1/a = 1/(a^n)

Consider the example

2^(-3) = (1/2)^3 = 1/2*1/2*1/2 = 1/(2^3) = 1/8 = 0,125

n = -1, -2, -3, etc.

To compute the negative

**degree**numbers must be omitted in the denominator.a^(-n) = (1/a)^n = 1/a*1/a*1/a* ... *1/a = 1/(a^n)

Consider the example

2^(-3) = (1/2)^3 = 1/2*1/2*1/2 = 1/(2^3) = 1/8 = 0,125

3

As can be seen from the example, -3

1) First calculate the fraction 1/2 = 0,5; and then to build in

ie 0,5^3 = 0,5*0,5*0,5 = 0,125

2) First build in the denominator

**the degree**of the number 2 can be calculated in different ways.1) First calculate the fraction 1/2 = 0,5; and then to build in

**a degree of**3,ie 0,5^3 = 0,5*0,5*0,5 = 0,125

2) First build in the denominator

**degree**2^3 = 2*2*2 = 8, and then calculate the fraction 1/8 = 0,125.4

Now compute -1

a^(-1) = (1/a)^1 = 1/(a^1) = 1/a

For example, let's build the number 5 to -1

5^(-1) = (1/5)^1 = 1/(5^1) = 1/5 = 0,2.

**degree**for the number, i.e., n = -1. The rules discussed above are suitable for this case.a^(-1) = (1/a)^1 = 1/(a^1) = 1/a

For example, let's build the number 5 to -1

**degree**5^(-1) = (1/5)^1 = 1/(5^1) = 1/5 = 0,2.

5

From the example clearly shows that the number -1 is the inverse fraction of the number.

Imagine the number 5 as a fraction 5/1, then 5^(-1) arithmetically not take it and immediately write the inverse of 5/1 is 1/5.So, 15^(-1) = 1/15,

6^(-1) = 1/6,

25^(-1) = 1/25

Imagine the number 5 as a fraction 5/1, then 5^(-1) arithmetically not take it and immediately write the inverse of 5/1 is 1/5.So, 15^(-1) = 1/15,

6^(-1) = 1/6,

25^(-1) = 1/25

Note

When raising a number to a negative exponent, it should be remembered that the number can't be zero. According to the rule, we need to lower the number in the denominator. And zero cannot be the denominator, because zero cannot be split.

Useful advice

Sometimes when working with degrees for ease of calculation, the fractional number of specially replace the integer to -1 degree

1/6 = 6^(-1)

1/52 = 52^(-1).

1/6 = 6^(-1)

1/52 = 52^(-1).

# Advice 4 : How to put a negative number in degree

The operation of raising to

**a degree**is binary, i.e. has two required input arguments and one output. One of the initial parameters is called the exponent determines the number of times that a multiplication operation needs to be applied to the second parameter - the base. The base can be both positive and negative**numbers**.Instruction

1

Use the exponentiation of a negative number are common to the operation of the rule. As for positive integers, exponentiation means multiplying the original value by itself the number of times per unit less the exponent. For example, to build in the fourth degree, the number -2, it must three times to multiply by itself: -2⁴=-2*(-2)*(-2)*(-2)=16.

2

Multiplying two negative numbers always gives a positive value, and the result for values with different signs is negative. From this we can conclude that in the construction of negative values in the degree with even index should always be positive, and at odd indices of the result will always be less than zero. Use this property to check of the calculations. For example, the -2 in the fifth degree should be a negative number -2⁵=-2*(-2)*(-2)*(-2)*(-2)=-32, and -2 in the sixth, positive -2⁶=-2*(-2)*(-2)*(-2)*(-2)*(-2)=64.

3

During the construction of the negative of the power index can be given in the format of fractions, for example, -64 to degree⅔. This figure means that the original value be raised to the degree equal to the numerator, and extract the root degree equal to the denominator. One part of this operation, considered in the previous steps, but here you should pay attention to another.

4

The root is an odd function, that is, for negative real numbers it can only be used for odd exponent. Even if this feature does not matter. So, if you need to build a negative number to a fractional degree with an even denominator, then the problem has no solution. In all other cases, do the first transaction from the first two steps, using as the exponent of the numerator of the fraction, and then extract the root with the degree of the denominator.