Multi-step Exponent Law Practice

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MULTI-STEP EXPONENT LAW PRACTICE

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The concepts for this exercise are summarized below. For a complete discussion, read the text.

EXPONENT LAWS
Let x , y , m and n be real numbers, with the following exceptions:

a base and exponent cannot simultaneously be zero (since 00 is undefined);
division by zero is not allowed;
for non-integer exponents (like 12 or 0.4 ), assume that bases are positive.

Then,

xm xn =xm+ n	Verbalize: same base, things multiplied, add the exponents
x mx n= xm-n	Verbalize: same base, things divided, subtract the exponents
(x m)n =x mn	Verbalize: something to a power, to a power; multiply the exponents
(xy) m =xm ym	Verbalize: product to a power; each factor gets raised to the power
(x y)m =x my m	Verbalize: fraction to a power; both numerator and denominator get raised to the power

EXAMPLES:

(1 x2 )3 =xp   where   p=-6

(x 2x3 )5= xp   where   p=-5

( x 2⁢x4 )-1 =x p   where   p=-6

x 2⁢x-3 x 5⁢ =xp   where   p=-6

x 2x 3⁢ x4 =xp   where   p=-5

( x 2 ) 3( x-1 ) 4 =x p   where   p=10

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Exponents and Power Rules