How do you find the value of #125^(-2/3)#?

Question

Eva Adamson · Accepted Answer

See the entire solution process below:

Using the exponents rule, we can first rewrite this expression as follows: #x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)# #125^(-2/3) = 125^(color(red)(1/3) xx color(blue)(-2)) = (125^color(red)(1/3))^color(blue)(-2)# Next, we can use the exponents and radicals rule to rewrite the term inside the parenthesis: #x^(1/color(red)(n)) = root(color(red)(n))(x)# #(125^color(red)(1/color(red)(3)))^color(blue)(-2) = (root(color(red)(3))(125))^color(blue)(-2) = 5^color(blue)(-2)# Now, finish the evaluation by applying this exponents rule: #x^color(blue)(a) = 1/x^color(blue)(-a)# #5^color(blue)(-2) = 1/5^color(blue)(- -2) = 1/5^2 = 1/25 = 0.04#

Avery Alexander · Answer

undefined To find the value of $125^{-\frac{2}{3}}$, you can use the property of exponents which states that $a^{-n} = \frac{1}{a^n}$.

So, $125^{-\frac{2}{3}} = \frac{1}{125^{\frac{2}{3}}}$.

Next, you can find the cube root of $125$ (which is $5$) and then raise it to the power of $2$.

Therefore, $125^{-\frac{2}{3}} = \frac{1}{(5)^2} = \frac{1}{25}$.

Hence, the value of $125^{-\frac{2}{3}}$ is $\frac{1}{25}$.