Integer Exponents and Scientific Notation: example 6.92

Simplify: ⓐ ${(−3)}^{−2}$ ⓑ $− 3^{−2}$ ⓒ ${(- \frac{1}{3})}^{−2}$ ⓓ $− {(\frac{1}{3})}^{−2} .$

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.

How did it go?

ⓐ Here the exponent applies to the base $−3$ .	${(−3)}^{−2}$
Take the reciprocal of the base and change the sign of the exponent.	$\frac{1}{{(−3)}^{−2}}$
Simplify.	$\frac{1}{9}$
ⓑ The expression $− 3^{−2}$ means "find the opposite of $3^{−2}$ ." Here the exponent applies to the base ${(- \frac{1}{3})}^{}$ .	$− 3^{−2}$
Rewrite as a product with $-1$ .	$−1 \cdot 3^{−2}$
Take the reciprocal of the base and change the sign of the exponent.	$−1 \cdot \frac{1}{3^{2}}$
Simplify.	$- \frac{1}{9}$
ⓒ Here the exponent applies to the base ${(- \frac{1}{3})}^{}$ .	${(- \frac{1}{3})}^{−2}$
Take the reciprocal of the base and change the sign of the exponent.	${(- \frac{3}{1})}^{2}$
Simplify.	$9$
ⓓ The expression $− {(\frac{1}{3})}^{−2}$ means "find the opposite of ${(\frac{1}{3})}^{−2}$ ." Here the exponent applies to the base $(\frac{1}{3})$ .
Rewrite as a product with $-1$ .	$−1 \cdot {(\frac{1}{3})}^{−2}$
Take the reciprocal of the base and change the sign of the exponent.	$−1 \cdot {(\frac{3}{1})}^{2}$
Simplify.	$−9$

ⓐ Here the exponent applies to the base $−3$ .	${(−3)}^{−2}$
Take the reciprocal of the base and change the sign of the exponent.	$\frac{1}{{(−3)}^{−2}}$
Simplify.	$\frac{1}{9}$
ⓑ The expression $− 3^{−2}$ means "find the opposite of $3^{−2}$ ." Here the exponent applies to the base ${(- \frac{1}{3})}^{}$ .	$− 3^{−2}$
Rewrite as a product with $-1$ .	$−1 \cdot 3^{−2}$
Take the reciprocal of the base and change the sign of the exponent.	$−1 \cdot \frac{1}{3^{2}}$
Simplify.	$- \frac{1}{9}$
ⓒ Here the exponent applies to the base ${(- \frac{1}{3})}^{}$ .	${(- \frac{1}{3})}^{−2}$
Take the reciprocal of the base and change the sign of the exponent.	${(- \frac{3}{1})}^{2}$
Simplify.	$9$
ⓓ The expression $− {(\frac{1}{3})}^{−2}$ means "find the opposite of ${(\frac{1}{3})}^{−2}$ ." Here the exponent applies to the base $(\frac{1}{3})$ .
Rewrite as a product with $-1$ .	$−1 \cdot {(\frac{1}{3})}^{−2}$
Take the reciprocal of the base and change the sign of the exponent.	$−1 \cdot {(\frac{3}{1})}^{2}$
Simplify.	$−9$