Question

Simplify the expression. (−3)^−4

Answer 1

1/81

Explanation:

In the problem, we are given the expression
`\displaystyle \large{(-3)^(-4)}`. To simplify this expression, we have to use laws of exponents since we cannot directly evaluate negative exponent by default. The law of exponent specifically for this expression is:

`\displaystyle \large{a^(-n)=(1)/(a^n)}`

Apply the formula to our given expression in.

`\displaystyle \large{(-3)^(-4)=(1)/((-3)^4)}`

Evaluate the expression.

`\displaystyle \large{(-3)^(-4)=(1)/((-3)(-3)(-3)(-3))}\\\\\displaystyle \large{(-3)^(-4)=(1)/(81)}`

Always keep in mind that for
`\displaystyle \large{a^(2n)}` when
`\displaystyle \large{a \in \mathbb{R}}` and
`\displaystyle \large{n \in \mathbb{I} - \{0\}}` the expression will always remain positive.

Please let me know if you have any questions!