Write $$ \sqrt{\left(\frac{3}{4}\right)^{9}} $$ as a power

Question

UpStudy AI · Accepted Answer

Given the expression

$$
\sqrt{\left(\frac{3}{4}\right)^{9}}
$$

we begin by rewriting the square root as an exponent of $$\frac{1}{2}$$. Thus, the expression becomes

$$
\left(\left(\frac{3}{4}\right)^{9}\right)^{\frac{1}{2}}.
$$

Next, we use the exponentiation rule $$\left(a^b\right)^c = a^{bc}$$, where in this case $$a = \frac{3}{4}$$, $$b = 9$$, and $$c = \frac{1}{2}$$. Multiplying the exponents gives

$$
9 \times \frac{1}{2} = \frac{9}{2}.
$$

Therefore, the expression can be written as

$$
\left(\frac{3}{4}\right)^{\frac{9}{2}}.
$$
$$ \left(\frac{3}{4}\right)^{\frac{9}{2}} $$

Write as a power

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