(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)

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

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

(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) $\sqrt[6]{b}$

View step-by-step help

Home

Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

\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 $\sqrt[6]{b} = b^{\frac{1}{6}}$ .