How do you evaluate and simplify $(120^(-2/5)*120^(2/5))/7^(-3/4)$ ?

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Answer 1 · 2017-07-27T03:15:53

See a solution process below:

First, use these rules of exponents to simplify the numerator:

$x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))$ and $a^color(red)(0) = 1$

$(120^color(red)(-2/5) * 120^color(blue)(2/5))/7^(-3/4) => 120^(color(red)(-2/5)+color(blue)(2/5))/7^(-3/4) =>$

$120^color(red)(0)/7^(-3/4) => 1/7^(-3/4)$

Next, we will use this rule to rewrite the expression:

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

$1/7^color(red)(-3/4) = 7^color(red)(- -3/4) = 7^(3/4)$

Then, we can rewrite the expression as:

$7^(3 xx 1/4)$

Now, we can use this rule of exponents to continue the simplification:

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

$7^(color(red)(3) xx color(blue)(1/4)) => (7^color(red)(3))^color(blue)(1/4) => 343^(1/4)$

Or, using this rule: $x^(1/color(red)(n)) = root(color(red)(n))(x)$

$root(4)(343)$

How do you evaluate and simplify (120^(-2/5)*120^(2/5))/7^(-3/4)(120^(-2/5)*120^(2/5))/7^(-3/4)?