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What is the value of \(\left(\frac{9}{16}\right)^{-\frac{3}{2}}\)?
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Answer and explanation
Correct answer: \(\frac{64}{27}\)
Since \(\left(\frac{9}{16}\right)^{\frac{1}{2}}=\frac{3}{4}\), \(\left(\frac{9}{16}\right)^{-\frac{3}{2}}=\left(\frac{3}{4}\right)^{-3}=\frac{64}{27}\). In exams, take the square root, cube, and invert.
Frequently asked questions
What is the correct answer to this question?
\(\frac{64}{27}\)
Why is this the correct answer?
Since \(\left(\frac{9}{16}\right)^{\frac{1}{2}}=\frac{3}{4}\), \(\left(\frac{9}{16}\right)^{-\frac{3}{2}}=\left(\frac{3}{4}\right)^{-3}=\frac{64}{27}\). In exams, take the square root, cube, and invert.
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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