Question
The expontential form for $(-2)^4\times\Big(\frac{5}{2}\Big)^4$ is $5^4$.
✓
Answer
Using law of exponents, $a^m \div a^n=(a)^{m-n}$ and $\Big(\frac{\text{a}}{\text{b}}\Big)^\text{m}=\frac{\text{a}^\text{m}}{\text{b}^\text{m}}$
[$\because a$ and $b$ are non-integers]
$\therefore$ $(-2)^4\times\Big(\frac{5}{2}\Big)^4=(2)^4\times\frac{(5)^4}{(2)^4}$
$=(2)^{4-4}\times5^4$
$=2^0\times5^4=5^4$ [$\because$ $(-a^m) = (a^m)$, if $m$ is an even number]
[$\because a$ and $b$ are non-integers]
$\therefore$ $(-2)^4\times\Big(\frac{5}{2}\Big)^4=(2)^4\times\frac{(5)^4}{(2)^4}$
$=(2)^{4-4}\times5^4$
$=2^0\times5^4=5^4$ [$\because$ $(-a^m) = (a^m)$, if $m$ is an even number]
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