# MULTIPLICATION PROPERTIES OF EXPONENTS WORKSHEET

Simplify :

1)  32  35

2)  52  4-2  55  46

3)  a4  b a2

4)  x2  x  x-4

5)  (84)5

6)  (56)0

7)  (y2)-4 ⋅ y5

8)  (-5x)2

9)  -(5x)2

10)  (a-2 ⋅ b0)3

11)  (p2q3)⋅ (p2q4)-4

12)  Light from the Sun travels at about 1.86 x 105 miles per second. It takes about 500 seconds for the light to reach  Earth. Find the approximate distance from the Sun to Earth. Give your answer in scientific notation.

=  32  35

Because the powers have the same base, keep the base and add the exponents.

=  32 + 3

=  35

=  52  4-2  55  46

Group powers with the same base together.

=  (52  55 (4-2  46)

Add the exponents of powers with the same base.

=  52 + 5  4-2 + 6

=  57  44

=  a4  b a2

Group powers with the same base together.

=  (a4  a2 b5

Add the exponents of powers with the same base.

=  a4 + 2  b5

=  a6  b5

=  x2  x  x-4

Because the powers have the same base, keep the base and add the exponents.

=  x2 + 1 + (-4)

=  x2 + 1 - 4

=  x-1

=  1/x

=  (84)5

Use the Power of a Power Property.

=  8⋅ 5

=  820

=  (56)0

Use the Power of a Power Property.

=  5⋅ 0

=  50

=  1

=  (y2)-4 ⋅ y5

Use the Power of a Power Property.

=  y-8 ⋅ y5

=  y-8 + 5

=  y-3

=  1/y3

=  (-5x)2

Use the Power of a Product Property.

=  (-5)⋅ x2

=  25x2

=  -(5x)2

Use the Power of a Product Property.

=  -(5⋅ x2)

=  -(25 ⋅ x2)

=  -25x2

=  (a-2 ⋅ b0)3

Use the Power of a Product Property.

=  (a-2)3 ⋅ (b0)3

=  a-2 ⋅ 3 ⋅ b⋅ 3

=  a-6 ⋅ b0

=  x-6 ⋅ 1

=  1/a6

=  (p2q3)⋅ (p2q4)-4

Use the Power of a Power Property.

=  (p2)4 ⋅ (q3)⋅ (p2)-4 ⋅ (q4)-4

=  p8 ⋅ q12 ⋅ p-8 ⋅ q-16

Group powers with the same base together.

=  (p8 ⋅ p-8) ⋅ (q12 ⋅ q-16)

Add the exponents of powers with the same base.

=  p8 + (-8) ⋅ q12 + (-16)

=  p8 - 8 ⋅ q12 - 16

=  p0 ⋅ q-4

=  1 ⋅ q-4

=  1/q4

Distance  =  Rate x Time

=  (1.86 x 105) x 500

Write 500 in scientific notation.

=  (1.86 x 105) x (5 x 102)

Use the Commutative and Associative Properties to group.

=  (1.86 x 5) x (105 x 102)

Multiply within each group.

=  9.3 x 105 + 2

=  9.3 x 107

The Sun is about 9.3 x 107 miles from Earth.

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