2 years ago

Simplify the expression. (−3)^−4

Mathematics

1 answer:

vova2212 [387]2 years ago

3 0

Answer:

1/81

Step-by-step 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:

$\displaystyle \large{a^{-n}=\dfrac{1}{a^n}}$

Apply the formula to our given expression in.

$\displaystyle \large{(-3)^{-4}=\dfrac{1}{(-3)^4}}$

Evaluate the expression.

$\displaystyle \large{(-3)^{-4}=\dfrac{1}{(-3)(-3)(-3)(-3)}}\\\\\displaystyle \large{(-3)^{-4}=\dfrac{1}{81}}$

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.