The correct option is B 1/4(1/4)^ 2÷(1/4)^ 3 =(1/4)^ 2+3 (∵a^m/a^n=a^m n) =(1/4)^1=1/4 ...

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Standard VIII

Mathematics

Powers with like Bases

1/4-2÷1/4-3=

Question

${(\frac{1}{4})}^{- 2} \div {(\frac{1}{4})}^{- 3} =$

\frac{1}{4}

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\frac{1}{4}

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\frac{1}{2}

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Solution

The correct option is B $\frac{1}{4}$
${(\frac{1}{4})}^{- 2} \div {(\frac{1}{4})}^{- 3}$
$= {(\frac{1}{4})}^{- 2 + 3} (∵ \frac{a^{m}}{a^{n}} = a^{m - n})$
$= {(\frac{1}{4})}^{1} = \frac{1}{4}$

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Question 22

Which of the following is an example of distributive property of multiplication over addition for rational numbers.
(a) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = [- \frac{1}{4} \times \frac{2}{3}] + [- \frac{1}{4} \times (\frac{- 4}{7})]$
(b) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = [\frac{1}{4} \times \frac{2}{3}] - (\frac{- 4}{7})$
(c) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = \frac{2}{3} + (- \frac{1}{4}) \times \frac{- 4}{7}$
(d) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = {\frac{2}{3} + (\frac{- 4}{7})} - \frac{1}{4}$