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(b^((3)/(4)))^((2)/(9))
Which of the following expressions is equivalent to the given expression?
Choose 1 answer:
(A)
sqrt(b^(6))
(B)
(2)/(9)root(4)(b^(3))
(c)
root(13)(b^(5))
(D)
root(6)(b)

$\left(b^{\frac{3}{4}}\right)^{\frac{2}{9}}$ $\newline$ Which of the following expressions is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $\sqrt{b^{6}}$ $\newline$ (B) $\frac{2}{9} \sqrt[4]{b^{3}}$ $\newline$ (c) $\sqrt[13]{b^{5}}$ $\newline$ (D) $\sqrt[6]{b}$

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Compare linear and exponential growth

Full solution

Q.

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

\newline

Which of the following expressions is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

\sqrt{b^{6}}

\newline

(B)

\frac{2}{9} \sqrt[4]{b^{3}}

\newline

(c)

\sqrt[13]{b^{5}}

\newline

(D)

\sqrt[6]{b}

Apply power of power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{(m*n)}$ . We will apply this rule to the given expression $(b^{\frac{3}{4}})^{\frac{2}{9}}$ . $\newline$ Calculation: $(b^{\frac{3}{4}})^{\frac{2}{9}} = b^{(\frac{3}{4}*\frac{2}{9})}$
Multiply exponents: Multiply the exponents. $\newline$ We need to multiply the fractions $(\frac{3}{4})$ and $(\frac{2}{9})$ to find the new exponent for $b$ . $\newline$ Calculation: $(\frac{3}{4}) \times (\frac{2}{9}) = \frac{6}{36} = \frac{1}{6}$
Write expression with new exponent: Write the expression with the new exponent. $\newline$ Now that we have the new exponent, we can write the expression as $b^{\frac{1}{6}}$ . $\newline$ Calculation: $(b^{\frac{3}{4}})^{\frac{2}{9}} = b^{\frac{1}{6}}$
Match expression to answer choices: Match the expression to the answer choices. $\newline$ We need to find which answer choice is equivalent to $b^{\frac{1}{6}}$ . $\newline$ (A) $\sqrt{b^6}$ is not equivalent because $\sqrt{b^6} = b^3$ . $\newline$ (B) $\left(\frac{2}{9}\right)\sqrt[4]{b^3}$ is not equivalent because it suggests a multiplication by $\left(\frac{2}{9}\right)$ , which is not present in our expression. $\newline$ (C) $\sqrt[13]{b^5}$ is not equivalent because it has a different root and exponent. $\newline$ (D) $\sqrt[6]{b}$ is equivalent because $\sqrt[6]{b} = b^{\frac{1}{6}}$ .

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\newline

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f(x)

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\newline

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\newline

Simplify any fractions.

\newline

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p(x)

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\newline

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\newline

Simplify any fractions.

\newline

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\newline

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\newline

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\newline

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\newline

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