Question

Simplify (5n^4)^−3. Assume n ≠ 0.

Answer 1

Since the exponent (-3) is negative, flip the expression to: 1/(5n^4)^3.

Notice how the negative exponent becomes positive as you flip it.

Now evaluate the powers in the denominator: 1/((5^3)(n^4)^3

I separated the constant (5) from the variable (n) to show you how the powers are evaluated.

1/(5x5x5)(nxnxnxn)(nxnxnxn)(nxnxnxn)
—-> the power four means that there are 4 multiples of n in the parentheses. The power 3 corresponds to how many groups.

1/(125)(n^12)

= 1/125n^12