How do you simplify ${(2 m)}^{- 3}$ $(2m)^-3$ and write it using only positive exponents?

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How do you simplify ${(2 m)}^{- 3}$ $(2m)^-3$ and write it using only positive exponents?

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Answer 1 · 2017-04-23T02:20:19

See the entire solution process below:

Explanation:

First, use this rule of exponents to eliminate the negative exponent:

$x^{a} = \frac{1}{x^{- a}}$ $x^color(red)(a) = 1/x^color(red)(-a)$

${(2 m)}^{- 3} = \frac{1}{{(2 m)}^{- - 3}} = \frac{1}{{(2 m)}^{3}}$ $(2m)^color(red)(-3) = 1/(2m)^color(red)(- -3) = 1/(2m)^3$

Next, use these two rules of exponents to complete the simplification:

$a = a^{1}$ $a = a^color(red)(1)$ and ${(x^{a})}^{b} = x^{a \times b}$ $(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))$

$\frac{1}{{(2 m)}^{3}} \Rightarrow \frac{1}{{(2^{1} m^{1})}^{3}} \Rightarrow \frac{1}{2^{1 \times 3} m^{1 \times 3}} \Rightarrow \frac{1}{2^{3} m^{3}} \Rightarrow \frac{1}{8 m^{3}}$ $1/(2m)^3 => 1/(2^color(red)(1)m^color(red)(1))^color(blue)(3) => 1/(2^(color(red)(1) xx color(blue)(3))m^(color(red)(1) xx color(blue)(3))) => 1/(2^3m^3) => 1/(8m^3)$

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How do you simplify ${(2 m)}^{- 3}$ $(2m)^-3$ and write it using only positive exponents?

1 Answer

Explanation:

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