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   $p=-6$

$( x 2 x 3 ) 5 = x p$   where   $p=-5$

$( x 2 ⁢ x 4 ) -1 = x p$   where   $p=-6$

$x 2⁢x-3 x 5⁢ =xp$   where   $p=-6$

$x 2 x 3 ⁢ x 4 =xp$   where   $p=-5$

$(x2) 3 (x-1) 4 =x p$   where   $p=10$