# FINDING THE VALUE OF A POWER

Finding the value of a power :

To find the value of a power, remember that the exponent indicates how many times to use the base as a factor.

Let us look into the examples given below to understand the concept.

## Finding the value of a power - Examples

Example 1 :

Find the value of 5³

Solution :

To find the value of 5³, we have to multiply the base 3 times.

That is,

5³ = 5 x 5 x 5

5 x 5 x 5 = 125

Hence, the value of 5³ =  125

## Value of a number to the zero power

The value of any non zero number raised to the power zero is 1.

For example,

10⁰  =  1

2⁰  =  1

The base can have any positive or negative integer, decimal, fraction or variable.

## Exponents with decimal and fractional bases

Now let us see some examples to understand how to find the value of power whose base are decimal and fraction

Example 2 :

Find the value of (0.4)²

Solution :

Base factor is 0.4 and the power is 2. To find the value of (0.4)², we have to multiply 0.4 two times.

That is,

(0.4)²  =  0.4 x 0.4

=  0.16

Example 3 :

Find the value of (2/5)³

Solution :

Base is (2/5) and the power is 3. To find the value of (2/5)³, we have to multiply (2/5) three times.

That is,

(2/5)³  =  (2/5) x (2/5) x (2/5)

By multiplying numerators we get 8. By multiplying the denominators we get 125.

Hence the value of (2/5)³ is 8/125.

## Exponents with negative bases

Whenever we want to find the value of exponents with negative base, first we have to check the power whether is odd or even.

(i) If the power is odd, then the answer will be negative.

(ii) If the power is even, then the answer will be positive.

Example 4 :

Find the value of (-7)³

Solution :

Base is -7 and the power is 3.

Hence, the value of  (-7)³ = -343

## Negative base and negative exponent

Whenever we want to find the value with negative base and negative exponent, first we have convert the power as positive.

For that we have to write the reciprocal form of the base and change the power as positive.

Example 5 :

Find the value of (-2)³

Solution :

Base is -2 and the power is -3.

(-1/2)³ = - (1/2) x (1/2) x (1/2) = -1/8

Since the power is odd.The answer will have negative sign.

## Related Topics

After having gone through the stuff given above, we hope that the students would have understood "Finding the value of a power".

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