Question
$\Big(\frac{2}{5}\Big)^{3}\div\Big(\frac{5}{2}\Big)^{3}=1$
✓
Answer
False.
Solution:
Here, $\Big(\frac{2}{5}\Big)^{3}\div\Big(\frac{5}{2}\Big)^{3}$ $\big[\because=\Big(\frac{\text{a}}{\text{b}}\Big)+\Big(\frac{\text{c}}{\text{d}}\Big)=\frac{\text{a}}{\text{b}}\times\frac{\text{d}}{\text{c}}\big]$
$=\Big(\frac{2}{5}\Big)^{3}\times\Big(\frac{2}{5}\Big)^{3}$ $\big[\because\text{a}^{\text{m}}\times\text{a}^{\text{n}}=\text{a}\text{}^{\text{m+n}}\big]$
$\Big(\frac{2}{5}\Big)^{3+3}=\Big(\frac{5}{2}\Big)^{6}$
Here, $\Big(\frac{2}{5}\Big)^{3}\div\Big(\frac{5}{2}\Big)^{3}\neq1$
Solution:
Here, $\Big(\frac{2}{5}\Big)^{3}\div\Big(\frac{5}{2}\Big)^{3}$ $\big[\because=\Big(\frac{\text{a}}{\text{b}}\Big)+\Big(\frac{\text{c}}{\text{d}}\Big)=\frac{\text{a}}{\text{b}}\times\frac{\text{d}}{\text{c}}\big]$
$=\Big(\frac{2}{5}\Big)^{3}\times\Big(\frac{2}{5}\Big)^{3}$ $\big[\because\text{a}^{\text{m}}\times\text{a}^{\text{n}}=\text{a}\text{}^{\text{m+n}}\big]$
$\Big(\frac{2}{5}\Big)^{3+3}=\Big(\frac{5}{2}\Big)^{6}$
Here, $\Big(\frac{2}{5}\Big)^{3}\div\Big(\frac{5}{2}\Big)^{3}\neq1$
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