Basic Practice with the Exponent Law "Negative Power, Gives a Flip"

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PRACTICE WITH 1/x ^p = x ^-p

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The concepts for this exercise are summarized below. For a complete discussion, read the text.
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Recall that x- 1=1 x ;
i.e., x- 1 is the reciprocal of x .

It follows, using the exponent laws, that

x -p = ( xp ) -1 = 1x p ;

i.e., x- p is the reciprocal of xp .

Continuing, it's convenient to notice that expressions of the form xm
can be moved from numerator to denominator, or from denominator to numerator,
just by changing the sign of the exponent. For example:

1 x-3 =x 31 =x3 :    exponent was negative in denominator; is positive in numerator

1 x3 =x- 31 =x-3 :    exponent was positive in denominator; is negative in numerator

x3 =x 31 =1 x-3 :    exponent was positive in numerator; is negative in denominator

x- 3=x -3 1=1 x3 :    exponent was negative in numerator; is positive in denominator

All the exponent laws are stated below, for completeness.

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 / x³ = x ^p where p = -3
1 / x^-2 = x ^p where p = 2

PRACTICE WITH 1/x p = x -p

PRACTICE WITH 1/x ^p = x ^-p