POWER RULE OF EXPONENTS

Power rule of exponents :

Here we are going to see what are power rules of exponents.

Case 1 :

When we have a power for any number or variable raised to another power, then we have to multiply both the powers. Case 2 :

In case we have two monomials which are multiplying or dividing then we have to consider the power as common for both terms.So we have to distribute the power. Case 3 :

In case we have negative power then we have to take the reciprocal of the given term and change negative power as positive.

3-1  =  1/3 (Reciprocal of 3 is 1/3)

(2/5)-7  =  (5/2)7 (Reciprocal of 2/5 is 5/2)

Case 4 :

Anything to the power zero is 1. Power rule of exponents - Examples

Example 1 :

Simplify (6 t6)2

Solution :

=  (6 t6)2

Here the power 2 is common for both 6 and t^6.Since it is multiplying, we have to distribute the power for both terms.

=  62 (t6)2

=  36 t(6 x 2)

=  36 t12

Example 2 :

Simplify (2/u)5

Solution :

=  (2/u)5

Here the power 5 is common for both numerator and denominator.

=  (25 / u5)

=  (32/u5)

Example 3 :

Simplify (5c7)2

Solution :

=  (5c7)2

Here the power 2 is common for both 5 and c7

=  52 (c7)2

=  (5 x 5)[ c(7 x 2) ]

=  25 c14

Example 4 :

Simplify (10 t3)2

Solution :

=  (10 t3)2

Here the power 2 is common for both 10 and t3

=  102 (t3)2

=  (10 x 10)[ t(3 x 2) ]

=  100 t6

Example 5 :

Simplify the expression given below.

4³· 5³

Solution :

Using power of a product property, we can simplify the given expression.

4³· 5³  =  (4 · 5)³

4³· 5³  =  20³

4³· 5³  =  8000

Example 6 :

Simplify the expression given below.

128· 128

Solution :

Using zero exponent property, we can simplify the given expression.

128· 128  =  1 · 128

128· 128  =  128

Example 7 :

Simplify the expression given below.

5³

Solution :

Using negative exponent property, we can simplify the given expression.

5³  =  1/5³

=  1/125

Example 8 :

Simplify the expression given below.

(a1/2)3/2

Solution :

When we have power raised to another power, we have to multiply both powers.

(a1/2)3/2  =  a(1/2)(3/2)

=  a(3/4)

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