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((j^(15))/(8))^((2)/(3))
Which of the following expressions is equivalent to the given expression?
Choose 1 answer:
(A)
(j^(10))/(4)
(B)
(j^(30))/(512)
(C)
(j^(10))/(8)
(D)
(j^(30))/(8)

$\left(\frac{j^{15}}{8}\right)^{\frac{2}{3}}$ $\newline$ Which of the following expressions is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{j^{10}}{4}$ $\newline$ (B) $\frac{j^{30}}{512}$ $\newline$ (C) $\frac{j^{10}}{8}$ $\newline$ (D) $\frac{j^{30}}{8}$

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Compare linear and exponential growth

Full solution

Q.

\left(\frac{j^{15}}{8}\right)^{\frac{2}{3}}

\newline

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

\newline

Choose

1

answer:

\newline

(A)

\frac{j^{10}}{4}

\newline

(B)

\frac{j^{30}}{512}

\newline

(C)

\frac{j^{10}}{8}

\newline

(D)

\frac{j^{30}}{8}

Understand expression and properties: Understand the given expression and the properties of exponents that can be applied. $\newline$ The given expression is $\left(\frac{j^{15}}{8}\right)^{\frac{2}{3}}$ . We can apply the property of exponents that states $\left(a^{\frac{m}{n}}\right) = \left(a^m\right)^{\frac{1}{n}}$ or the $n$ th root of $a^m$ .
Apply exponent rule: Apply the exponent rule to the given expression. $\newline$ We can rewrite the expression as $(j^{15 \cdot (\frac{2}{3})})/(8^{\frac{2}{3}})$ . This simplifies the exponentiation by distributing the $(\frac{2}{3})$ exponent to both the numerator and the denominator.
Calculate new exponents: Calculate the new exponents for both the numerator and the denominator. $\newline$ For the numerator: $15 \times \left(\frac{2}{3}\right) = 10$ . $\newline$ For the denominator: $8^{\frac{2}{3}}$ is the cube root of $8$ squared, which is $2^2$ since $8$ is $2^3$ . So, $8^{\frac{2}{3}} = 2^2 = 4$ .
Rewrite expression with new exponents: Rewrite the expression with the new exponents. $\newline$ The expression now becomes $\frac{j^{10}}{4}$ .
Match simplified expression with choices: Match the simplified expression with the given choices. $\newline$ The expression $(j^{10})/4$ corresponds to choice (A) $(j^{10})/(4)$ .

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