Evaluate (27/8)^-2/3.

Simplification & Approximation · Question 47 of 71

Question 47

MediumOriginal question

Evaluate $\left(\frac{27}{8}\right)^{-\frac{2}{3}}$ .

\frac{3}{2}

Correct answerYour answer

\frac{2}{3}

Correct answerYour answer

\frac{4}{9}

Correct answerYour answer

\frac{9}{4}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The negative sign flips the fraction: $\left(\frac{8}{27}\right)^{\frac{2}{3}}$ .
The 3 in the denominator of the power means cube root: $\sqrt[3]{\frac{8}{27}} = \frac{2}{3}$ .
The 2 means square: $\left(\frac{2}{3}\right)^2 = \frac{4}{9}$ .

Worth noting

Ignoring the minus sign gives $\frac{9}{4}$ ; stopping after the cube root gives $\frac{2}{3}$ .

Ten questions from Simplification & Approximation, at your own pace.

Ten questions from Simplification & Approximation, at your own pace.