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Exponents and Powers — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSExponents and Powers2 Marks
Question
Simplify: $\left\{\left(\frac{1}{3}\right)^{-2}-\left(\frac{1}{2}\right)^{-3}\right\} \div\left(\frac{1}{4}\right)^{-2}$
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Answer

$\left\{\left(\frac{1}{3}\right)^{-2}-\left(\frac{1}{2}\right)^{-3}\right\} \div\left(\frac{1}{4}\right)^{-2}$
= $\left\{\frac{1^{-2}}{3^{-2}}-\frac{1^{-3}}{2^{-3}}\right\} \div \frac{1^{-2}}{4^{-2}}$
= $\left\{\frac{3^{2}}{1^{2}}-\frac{2^{3}}{1^{3}}\right\} \div \frac{4^{2}}{1^{2}}=\{9-8\} \div 16=\frac{1}{16}$

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