Given; (1/4)^2×1/4.Now,(1/4)^2×1/4= 1/4×1/4×1/4 =1/64Hence, (1/4)^2×1/4= 1/64. ...

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Byju's Answer

Standard VII

Mathematics

Multiplying Powers with the Same Base

Simplify : 1/...

Question

Simplify :
${(\frac{1}{4})}^{2} \times \frac{1}{4}$

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Solution

Given; ${(\frac{1}{4})}^{2} \times \frac{1}{4}$ .
Now,
${(\frac{1}{4})}^{2} \times \frac{1}{4} = \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4}$
$= \frac{1}{64}$
Hence, ${(\frac{1}{4})}^{2} \times \frac{1}{4} = \frac{1}{64}$ .

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Find the value of $x$ so that;
$(i) {(\frac{3}{4})}^{2 x + 1} = {({(\frac{3}{4})}^{3})}^{3}$
$(i i) {(\frac{2}{5})}^{3} \times {(\frac{2}{5})}^{6} = {(\frac{2}{5})}^{3 x}$
$(i i i) {(- \frac{1}{5})}^{20} \div {(- \frac{1}{5})}^{15} = {(- \frac{1}{5})}^{5 x}$
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Simplify : 142×14

Given; 142×14.Now,142×14=14×14×14 =164Hence, 142×14=164.

Simplify :
${(\frac{1}{4})}^{2} \times \frac{1}{4}$

Given; ${(\frac{1}{4})}^{2} \times \frac{1}{4}$ .
Now,
${(\frac{1}{4})}^{2} \times \frac{1}{4} = \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4}$
$= \frac{1}{64}$
Hence, ${(\frac{1}{4})}^{2} \times \frac{1}{4} = \frac{1}{64}$ .