QuestionFind an equivalent expression for $\left(\left(\frac{3}{4}\right)^{4}\left(\frac{3}{4}\right)^{3}\right)^{2}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\left(\left(\frac{3}{4}\right)^{4}\left(\frac{3}{4}\right)^{3}\right)^{}$ . . We are asked to find an equivalent expression from the given options.

STEP 2

We first simplify the expression inside the innermost parentheses. According to the laws of exponents, when we multiply two exponents with the same base, we add the powers.
$\left(\frac{}{4}\right)^{4}\left(\frac{}{4}\right)^{} = \left(\frac{}{4}\right)^{4+}$

STEP 3

Now, calculate the sum of the exponents.
$\left(\frac{3}{}\right)^{+3} = \left(\frac{3}{}\right)^{7}$

STEP 4

Now, we have the expression $\left(\left(\frac{3}{4}\right)^{7}\right)^{2}$ . According to the laws of exponents, when we raise a power to a power, we multiply the exponents.
$\left(\left(\frac{3}{4}\right)^{7}\right)^{2} = \left(\frac{3}{4}\right)^{7 \times2}$

STEP 5

Now, calculate the product of the exponents.
$\left(\frac{3}{4}\right)^{7 \times2} = \left(\frac{3}{4}\right)^{14}$ So, the equivalent expression for $\left(\left(\frac{3}{4}\right)^{4}\left(\frac{3}{4}\right)^{3}\right)^{2}$ is $\left(\frac{3}{4}\right)^{14}$ .

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