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Exponents and Powers — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSExponents and Powers1 Mark
Question
$\Big(\frac{4}{3}\Big)^{5}\times\Big(\frac{5}{7}\Big)^{5}=\Big(\frac{4}{3}+\frac{5}{7}\Big)^{5}$
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Answer

False.
Solution:
Here,$\Big(\frac{4}{3}\Big)^{5}\times\Big(\frac{5}{7}\Big)^{5}=\Big(\frac{4}{3}\times\frac{5}{7}\Big)^{5}$$\big[\because\text{a}^{\text{m}}\times\text{b}^{\text{m}}=(\text{ab})^{\text{m}}\big]$
and $\Bigg[\Big(\frac{4}{3}\Big)^{5}+\Big(\frac{5}{7}\Big)^{5}\Bigg]^{5}$ $\Big[=\Big(\frac{\text{a}}{\text{b}}\Big)+\Big(\frac{\text{c}}{\text{d}}\Big)=\frac{\text{a}}{\text{b}}\times\frac{\text{d}}{\text{c}}\Big]$
$=\Big(\frac{4}{3}\times\frac{5}{7}\Big)^{5}$
Hence, $\Big(\frac{4}{3}\times\frac{5}{7}\Big)^{5}\neq\Big(\frac{4}{3}\times\frac{7}{5}\Big)^{5}$

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