Integer Exponents and Scientific Notation: example 6.91

Simplify: ⓐ ${(\frac{5}{7})}^{−2}$ ⓑ ${(- \frac{2 x}{y})}^{−3} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify: ⓐ ${(\frac{2}{3})}^{−4}$ ⓑ ${(- \frac{6 m}{n})}^{−2} .$

How did it go?

ⓐ	${(\frac{5}{7})}^{−2}$
Use the Quotient to a Negative Exponent Property, ${(\frac{a}{b})}^{− n} = {(\frac{b}{a})}^{n}$ .
Take the reciprocal of the fraction and change the sign of the exponent.	${(\frac{7}{5})}^{2}$
Simplify.	$\frac{49}{25}$
ⓑ	${(- \frac{2 x}{y})}^{−3}$
Use the Quotient to a Negative Exponent Property, ${(\frac{a}{b})}^{− n} = {(\frac{b}{a})}^{n}$ .
Take the reciprocal of the fraction and change the sign of the exponent.	${(- \frac{y}{2 x})}^{3}$
Simplify.	$- \frac{y^{3}}{8 x^{3}}$

ⓐ	${(\frac{5}{7})}^{−2}$
Use the Quotient to a Negative Exponent Property, ${(\frac{a}{b})}^{− n} = {(\frac{b}{a})}^{n}$ .
Take the reciprocal of the fraction and change the sign of the exponent.	${(\frac{7}{5})}^{2}$
Simplify.	$\frac{49}{25}$
ⓑ	${(- \frac{2 x}{y})}^{−3}$
Use the Quotient to a Negative Exponent Property, ${(\frac{a}{b})}^{− n} = {(\frac{b}{a})}^{n}$ .
Take the reciprocal of the fraction and change the sign of the exponent.	${(- \frac{y}{2 x})}^{3}$
Simplify.	$- \frac{y^{3}}{8 x^{3}}$