Question

Simplify write your answers without exponents(THIS IS ONE QUESTION, I DO AN ONLINE MATH PROGRAM WHERE THIS IS CONSIDERED ONE QUESTION)

Answer 1

1. (1/125)^-2/3

Here are the steps in simplifying the given term.

a. Make the exponent positive by getting the reciprocal of the base.

`((1)/(125))^{-(2)/(3)}\Rightarrow(125)^{(2)/(3)}`

b. Get the cube root of 125.

`\sqrt[3]{125}=5`

c. Square the result in step b.

`5^2=5*5=25`

Therefore, (1/125)^-2/3 = 25.

2. 64^-2/3

To simplify this, we follow the same steps shown above.

a. Again, make the exponent positive by getting the reciprocal of the base.

`64^{-(2)/(3)}\Rightarrow((1)/(64))^{(2)/(3)}`

b. Get the cube root of 1/64.

`\sqrt[3]{(1)/(64)}=(1)/(4)`

c. Square the result in step b.

`((1)/(4))^2=(1)/(4)*(1)/(4)=(1)/(16)`

Hence, 64^-2/3 = 1/16.