What is the value of \(\left(\frac{27}{8}\right)^{2/3}\)?
Answer and explanation
Correct answer: \(\frac{9}{4}\)
Using the fractional exponent rule \(a^{m/n}=(\sqrt[n]{a})^m\), we get \(\left(\frac{27}{8}\right)^{2/3}=\left(\sqrt[3]{\frac{27}{8}}\right)^2=\left(\frac{3}{2}\right)^2=\frac{9}{4}\). Therefore, option A is correct. Option B is only the cube root, \(\frac{3}{2}\), and does not include the required square. Exam tip: for an exponent \(m/n\), take the \(n\)th root and then raise the result to the power \(m\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{9}{4}\)
Why is this the correct answer?
Using the fractional exponent rule \(a^{m/n}=(\sqrt[n]{a})^m\), we get \(\left(\frac{27}{8}\right)^{2/3}=\left(\sqrt[3]{\frac{27}{8}}\right)^2=\left(\frac{3}{2}\right)^2=\frac{9}{4}\). Therefore, option A is correct. Option B is only the cube root, \(\frac{3}{2}\), and does not include the required square. Exam tip: for an exponent \(m/n\), take the \(n\)th root and then raise the result to the power \(m\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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