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Exponent Laws Review 2

 

Multiplication and Division of Power 

 

 

Formula 1:         am x an = am + n

            For example, 23 x 25 = 23+5 = 28

Formula 2:          am ÷ an = am - n

            For example, 26 ÷ 23 = 26-3 = 23

NOTE: Formula 1 & 2 ONLY apply to the exponents with the SAME base

Formula 3:          (am)n = am x n

            For example, (25)2 = 25 x 2 = 210

Formula 4:          (ab)m = ambm

            For example, (3y)3 = 33y3

Formula 5:         (a / b)m = am / bm

            For example, (2/5)3 = 23 / 53

 

Zero Exponent

Every number, variable or unknown applied to the zero exponent will equal to 1.

For example,     30 = 1;   (x+3y)0 = 1;       (50000x)0 = 1

Negative Exponents

Formula 6:          a-m = 1 / am

            For example,     5-3 = 1/53                     

Formula 7:          (a / b)-m = (b / a)m

For example,     (2/3)-2 = (3/2)2

Sometimes, more than one formula may be used to solve a single problem, for example,

[(4a3b2)2 / x]-2

=          [(42a3 x 2 b2 x 2) / x]-2

=          [16a6b4 / x]-2

=          [x / 16a6b4]2

=          (x)2 / (16a6b4)2

=          x2 / 256a12b8

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