((64)/(b^(27)))^(-(2)/(3)) Which of the following is equivalent to the given expression? Choose 1 answer: (A) (b^(9))/(16) (B) (b^(18))/(16) (C) -(128b^(9))/(3) (D) -(128b^(18))/(3)

Simplify expression using exponents: Simplify the given expression using the properties of exponents. The expression ((64)/(b^(27)))^(-(2)/(3)) can be rewritten by applying the negative exponent rule, which states that a^(-n) = 1/(a^n). This gives us: (1/((64)/(b^(27)))^(2/3))Apply negative exponent rule: Simplify the expression inside the parentheses. The expression inside the parentheses is a fraction raised to a power. We can apply the exponent to both the numerator and the denominator separately: (1/((64^(2/3))/(b^(27*(2/3)))))Simplify expression inside parentheses: Calculate the exponent for the numerator. 64^(2/3) is the cube root of 64 squared. Since 64 is 4^3, we have: (4^3)^(2/3) = 4^(3*(2/3)) = 4^2 = 16Calculate numerator exponent: Calculate the exponent for the denominator. b^(27*(2/3)) is b raised to the power of 27 times 2/3, which simplifies to: b^(18)Calculate denominator exponent: Combine the simplified numerator and denominator. Now we have: 1/((16)/(b^(18))) = b^(18)/16Combine numerator and denominator: Match the simplified expression with the given choices. The expression b^(18)/16 corresponds to choice (B).

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((64)/(b^(27)))^(-(2)/(3))
Which of the following is equivalent to the given expression?
Choose 1 answer:
(A)
(b^(9))/(16)
(B)
(b^(18))/(16)
(C)
-(128b^(9))/(3)
(D)
-(128b^(18))/(3)

$\left(\frac{64}{b^{27}}\right)^{-\frac{2}{3}}$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{b^{9}}{16}$ $\newline$ (B) $\frac{b^{18}}{16}$ $\newline$ (C) $-\frac{128 b^{9}}{3}$ $\newline$ (D) $-\frac{128 b^{18}}{3}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

\left(\frac{64}{b^{27}}\right)^{-\frac{2}{3}}

\newline

Which of the following is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

\frac{b^{9}}{16}

\newline

(B)

\frac{b^{18}}{16}

\newline

(C)

-\frac{128 b^{9}}{3}

\newline

(D)

-\frac{128 b^{18}}{3}

Simplify expression using exponents: Simplify the given expression using the properties of exponents. $\newline$ The expression $(\frac{64}{b^{27}})^{-\frac{2}{3}}$ can be rewritten by applying the negative exponent rule, which states that $a^{-n} = \frac{1}{a^n}$ . This gives us: $\newline$ $\frac{1}{(\frac{64}{b^{27}})^{\frac{2}{3}}}$
Apply negative exponent rule: Simplify the expression inside the parentheses. $\newline$ The expression inside the parentheses is a fraction raised to a power. We can apply the exponent to both the numerator and the denominator separately: $\newline$ $(1/((64^{2/3})/(b^{27\cdot(2/3)})))$
Simplify expression inside parentheses: Calculate the exponent for the numerator. $\newline$ $64^{\frac{2}{3}}$ is the cube root of $64$ squared. Since $64$ is $4^3$ , we have: $\newline$ $(4^3)^{\frac{2}{3}} = 4^{3\cdot(\frac{2}{3})} = 4^2 = 16$
Calculate numerator exponent: Calculate the exponent for the denominator. $\newline$ $b^{27\left(\frac{2}{3}\right)}$ is $b$ raised to the power of $27$ times $\frac{2}{3}$ , which simplifies to: $\newline$ $b^{18}$
Calculate denominator exponent: Combine the simplified numerator and denominator. $\newline$ Now we have: $\newline$ $\frac{1}{\left(\frac{16}{b^{18}}\right)} = \frac{b^{18}}{16}$
Combine numerator and denominator: Match the simplified expression with the given choices. $\newline$ The expression $b^{18}/16$ corresponds to choice (B).