Respuesta :

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
abidemiokin

Inverse law of indices are written as negative indices. The resulting expression after simplification is [tex]\frac{1}{125n^{12}}[/tex]

Law of indices

According to the law of indices

[tex]a^{-n}=1/n[/tex]

Given the indices expression

[tex](5n^4)^{-3}[/tex]

This can be written as a fraction to have:

[tex](5n^4)^{-3} = \frac{1}{(5n^4)^3} \\(5n^4)^{-3} = \frac{1}{125n^{12}}[/tex]

Hence the resulting expression after simplification is [tex]\frac{1}{125n^{12}}[/tex]

Learn more on indices here: https://brainly.com/question/10339517

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