(27a^-3b^6c^3)^1/3

Question

I know the answer is (3b^2c)/a but I don't know the steps.

Answer 1

(27a^-3b⁶c³)^1/3

Raising something to the 1/3 power means taking the cube root.

 

Treat each of the factors in the parenthesis separately.

You are taking the cube root of each of the individual factors.

1. The cube root of 27 is 3

2. When you raise a variable with an exponent to a power, you multiply the exponent by the power (1/3).

So, multiply the exponent of each variable by the power (1/3)

You get a^-1b²c

Combining this with the constant, you get:

3a^-1b²c

At this point, you need to rewrite the expression with positive exponents. If a variable has a negative exponent, invert it

This gives us:

(3b²c)/a