Integer Exponents and Scientific Notation: example 10.72

Simplify: ${(5 x^{−3})}^{2} .$

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.

Simplify: ${(8 a^{−4})}^{2} .$

How did it go?

	${(5 x^{−3})}^{2}$
Use the Product to a Power Property, ${(a b)}^{m} = a^{m} b^{m} .$	$5^{2} {(x^{−3})}^{2}$
Simplify $5^{2}$ and multiply the exponents of $x$ using the Power Property, ${(a^{m})}^{n} = a^{m \cdot n} .$	$25 k^{−6}$
Rewrite $x^{−6}$ by using the definition of a negative exponent, $a^{- n} = \frac{1}{a^{n}} .$	$25 \cdot \frac{1}{x^{6}}$
Simplify	$\frac{25}{x^{6}}$

	${(5 x^{−3})}^{2}$
Use the Product to a Power Property, ${(a b)}^{m} = a^{m} b^{m} .$	$5^{2} {(x^{−3})}^{2}$
Simplify $5^{2}$ and multiply the exponents of $x$ using the Power Property, ${(a^{m})}^{n} = a^{m \cdot n} .$	$25 k^{−6}$
Rewrite $x^{−6}$ by using the definition of a negative exponent, $a^{- n} = \frac{1}{a^{n}} .$	$25 \cdot \frac{1}{x^{6}}$
Simplify	$\frac{25}{x^{6}}$