How do you simplify $1000^(-2/3)$ ?

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Answer 1 · 2017-07-30T12:09:17

See a solution process below:

First, we can use this rule for exponents to eliminate the negative exponent:

$x^color(red)(a) = 1/x^color(red)(-a)$

$1000^color(red)(-2/3) = 1/1000^color(red)(- -2/3) = 1/1000^color(red)(2/3)$

We can next rewrite the exponent as:

$1/1000^color(red)(2/3) = 1/1000^(1/3 xx 2)$

And then use this rule to rewrite the expression again:

$x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)$

$1/1000^(color(red)(1/3) xx color(blue)(2)) = 1/(1000^(color(red)(1/3)))^color(blue)(2)$

We can convert the term within the parenthesis to radical form using this rule:

$x^(1/color(red)(n)) = root(color(red)(n))(x)$

$1/(1000^(color(red)(1/3)))^color(blue)(2) = 1/(root(color(red)(3))(1000))^color(blue)(2) = 1/10^color(blue)(2) = 1/100$

How do you simplify 1000^(-2/3)1000^(-2/3)?