Question

What is the value of (Two-thirds) Superscript negative 4?

Answer 1

Option D: $\frac{81}{16}$ is the value of $\left(\frac{2}{3}\right)^{-4}$

Explanation:

The given expression is $\left(\frac{2}{3}\right)^{-4}$

We need to determine the value of the given expression.

To determine the value, let us simplify the expression.

Applying the exponent rule in the expression $a^{-b}=\frac{1}{a^{b}}$, we have,

$\frac{1}{\left(\frac{2}{3}\right)^{4}}$

Let us apply the exponent rule that $\left(\frac{a}{b}\right)^{c}=\frac{a^{c}}{b^{c}}$ , we get,

$\frac{1}{(\frac{2^{4}}{3^{4}})}$

Simplifying, we get,

$\frac{1}{(\frac{16}{81})}$

Let us apply the fraction rule that $\frac{1}{c}=\frac{c}{b}$ , we have,

$\frac{81}{16}$

Thus, the value of the expression $\left(\frac{2}{3}\right)^{-4}$ is $\frac{81}{16}$

Hence, Option D is the correct answer.

Answer 2

Answer:

D

Step-by-step explanation:

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