Question

The question, Please explain in steps below! xoxo

The equation if not clear below is: 8/125^-2/3

/ = the division symbol
^ = to the power of

$\frac{8}{125} ^{-2}{3}$

Answer 1

Answer:

  25/4

Step-by-step explanation:

We assume you mean ...

  $\left(\dfrac{8}{125}\right)^{-2/3}$

and you want it simplified. It helps to recognize that 8 and 125 are cubes.

  $\left(\dfrac{2^3}{5^3}\right)^{-2/3}=\left(\dfrac{2}{5}\right)^{-2}=\dfrac{5^2}{2^2}=\dfrac{25}{4}$

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The applicable rules of exponents are ...

  (a^b)^c = a^(b·c)

  a^(-b) = 1/(a^b)

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If you do this problem on a calculator, you need to pay attention to required grouping symbols, parentheses. Both the fraction and the exponent need to be enclosed in parentheses.

The problem you have written in text form (8/125^-2/3) is ...

  $\dfrac{\left(\dfrac{8}{125^{-2}}\right)}{3}=\dfrac{125000}{3}=41666\frac{2}{3}$