What is (64^{2/3})?
Answer and explanation
Correct answer: 16
Using the rule for fractional exponents, \(64^{2/3}=(\sqrt[3]{64})^2\). Since \(\sqrt[3]{64}=4\), we get \(4^2=16\). Therefore, option B is correct. Option A is only the cube root and does not include the required squaring. Exam tip: For \(a^{m/n}\), it is often easiest to take the \(n\)th root first and then raise the result to the \(m\)th power.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Using the rule for fractional exponents, \(64^{2/3}=(\sqrt[3]{64})^2\). Since \(\sqrt[3]{64}=4\), we get \(4^2=16\). Therefore, option B is correct. Option A is only the cube root and does not include the required squaring. Exam tip: For \(a^{m/n}\), it is often easiest to take the \(n\)th root first and then raise the result to the \(m\)th power.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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