# PROPERTIES OF EXPONENTS WORKSHEET

## About "Properties of exponents worksheet"

Properties of exponents worksheet :

Here we are going to see some practice questions on properties of exponents.

(1)  Simplify 2m2  2m3

(2)  Simplify m4  2m-3

(3)  Simplify (4a3)2

(4)  Simplify (x3)0

(5)  Simplify 4 ab 3 ab3

(6)  Simplify r2/2r3

(7)  Simplify 4x0y2z3/4x

(8)  Simplify (2xy4)4(xy)5

(9)  Simplify x-4/x-9

(10)  Simplify x-1/4x4

(11)  Simplify (x2y-1)4

(12)  Simplify x2y⋅ x3y2

## Properties of exponents worksheet - Solution

Example 1 :

Simplify 2m2  2m3

Solution :

=  2m2  2m3

=  4m(2+3)

=  4m5

Since we have same base for both terms, we put only one base and add the powers.

Hence the answer is 4m5

Example 2 :

Simplify m4  2m-3

Solution :

=  m4  2m-3

=  2m(4 - 3)

=  2m1

Since we have same base for both terms, we put only one base and combining the powers.

Hence the answer is 2m.

Example 3 :

Simplify (4a3)2

Solution :

=  (4a3)2

Since we have power 2 for both the terms 4 and a3, we need to distribute the power for both terms

=  42(a3)2

=  16a6

Hence the answer is 16a6

Example 4 :

Simplify (x3)0

Solution :

=  (x3)0

Since we have power zero, the answer must be 1.

Example 5 :

Simplify 4 ab 3 ab3

Solution :

=  4 ab 3 ab3

=  12 a(3+4)b(2+3)

=  12 a7b5

Hence the answer is 12 a7b5

Example 6 :

Simplify r2/2r3

Solution :

=   r2/2r3

=  (1/2) r(2-3)

=  (1/2) r-1

=  (1/2r)

Hence the answer is 1/2r.

Example 7 :

Simplify 4x0y2z3/4x

Solution :

=   4x0y2z3/4x

The value of anything to the power zero is 1. So, x0 is 1.

=   y2z3/x

Example 8 :

Simplify (2xy4)4(xy)5

Solution :

=   24x(y4)xy5

=   16 xy16 xy5

=   16 x(4 + 5) y(16 + 5)

=   16 xy21

Hence the answer is 16 xy21

Example 9 :

Simplify x-4/x-9

Solution :

=   x-4/x-9

=   x-4x9

=   x(-4 + 9)

=   x5

Hence the answer is  x5

Example 10 :

Simplify x-1/4x4

Solution :

=  x-1/4x4

=   (1/4) x (-1 + 4)

=   (1/4) x 3

=   1/4 x3

Hence the answer is 1/4 x3

Example 11 :

Simplify (x2y-1)4

Solution :

=  (x2y-1)4

=  (x2)(y-1)4

=  x8 y-4

=  x8 /y4

Hence the answer is x8 /y4

Example 12 :

Simplify x2y⋅ x3y2

Solution :

=  x2y⋅ x3y2

=  x(2 + 3) y(3+2)

=  x5 y5

Hence the answer is xy5

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