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What is the value of \(\left(\dfrac{27}{8}\right)^{-\frac{2}{3}}\)?
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Answer and explanation
Correct answer: (,\dfrac{4}{9},)
\(\left(\dfrac{27}{8}\right)^{\frac{1}{3}}=\dfrac{3}{2}\), so \(\left(\dfrac{27}{8}\right)^{-\frac{2}{3}}=\left(\dfrac{3}{2}\right)^{-2}=\dfrac{4}{9}\). In exams, take the reciprocal for a negative exponent.
Frequently asked questions
What is the correct answer to this question?
(,\dfrac{4}{9},)
Why is this the correct answer?
\(\left(\dfrac{27}{8}\right)^{\frac{1}{3}}=\dfrac{3}{2}\), so \(\left(\dfrac{27}{8}\right)^{-\frac{2}{3}}=\left(\dfrac{3}{2}\right)^{-2}=\dfrac{4}{9}\). In exams, take the reciprocal for a negative exponent.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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