# MULTIPLICATION WITH EXPONENTS

In this section, you will learn how to do binary operation multiplication between terms with exponents.

We can use Products of Powers property to multiply terms with exponents.

Products of Powers Property :

Words :

The product of two powers with the same base equals that base raised to the sum of the exponents.

Numbers :

58 ⋅ 54  =  58 + 4  =  512

Algebra :

If 'x' is any nonzero real number and 'm' and 'n' are integers, then,

xm ⋅ xn  =  xm + n

Example 1 :

Simplify :

34  33

Solution :

=  34  33

Product of Powers Property.

=  34 + 3

=  37

Example 2 :

Simplify :

5-5  53

Solution :

=  5-5  53

Product of Powers Property.

=  5-5 + 3

=  5-2

=  1/52

Example 3 :

Simplify :

76  7-4

Solution :

=  76  7-4

Product of Powers Property.

=  76 + (-4)

=  76 - 4

=  72

Example 4 :

Simplify :

9-2  9-5

Solution :

=  9-2  9-5

Product of Powers Property.

=  9-2 + (-5)

=  9-2 - 5

=  9-7

=  1/97

Example 5 :

Simplify :

(-2)-5  (-2)6

Solution :

=  (-2)-5  (-2)6

Product of Powers Property.

=  (-2)-5 + 6

=  (-2)1

=  -2

Example 6 :

Simplify :

(-4)5  (-4)8

Solution :

=  (-4)5  (-4)8

Product of Powers Property.

=  (-4)5 + 8

=  (-4)13

Because the exponent is an odd number, negative sign inside the parentheses will remain same.

=  -413

Example 7 :

Simplify :

(-7)9  (-7)5

Solution :

=  (-7)9  (-7)5

Product of Powers Property.

=  (-7)9 + 5

=  (-7)14

Because the exponent is an even number, negative sign inside the parentheses will become positive.

=  714

Example 8 :

Simplify :

42 ⋅ 3-2 ⋅ 4⋅ 36

Solution :

=  42 ⋅ 3-2 ⋅ 4⋅ 36

Group powers with the same base together.

=  (42 ⋅ 45⋅ (3-2 ⋅ 36)

Product of Powers Property.

=  42 + 5 ⋅ 3-2 + 6

=  47 ⋅ 34

Example 9 :

Simplify :

4P⋅ 2P3 ⋅ P4

Solution :

=  4P 2P3  P4

=  (4 ⋅ 2) ⋅ (P P3  P4)

Product of Powers Property.

=  8 ⋅ P5 + 3 + 4

=  8P12

Example 10 :

Find the value of x :

(2/8)2x   (2/8)x  =  (2/8)6

Solution :

(2/8)2x   (2/8)x  =  (2/8)6

Product of Powers Property.

(2/8)2x + x  =  (2/8)6

(2/8)3x  =  (2/8)6

If two powers are equal with the same base, then the exponents can be equated.

3x  =  6

Divide each side by 3.

x  =  2 Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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