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Leno4ka [110]
1 year ago
7

Simplify the expression. (−3)^−4

Mathematics
1 answer:
vova2212 [387]1 year 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.

Please let me know if you have any questions!

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