Question
By multiplying $\Big(\frac{5}{3}\Big)^4$ by ________ we get $5^4$.
✓
Answer
By multiplying $\Big(\frac{5}{3}\Big)^4$ by ________ we get $5^4$.
Solution:
Let $x$ be multiplied with $\Big(\frac{5}{3}\Big)^4$ to get $5^4$.
So,
$\Big(\frac{5}{3}\Big)^4\times\text{x}=5^4$
$\therefore$ $\text{x}=\frac{5^4}{\Big(\frac{5}{3}\Big)^4}$
$=5^4\times3^4\times5^{-4}=(5)^{4-4}\times3^4$ $\Big[\because\text{a}^{-\text{m}}=\frac{1}{\text{a}^\text{m}},\text{a}^\text{m}\times\text{a}^{\text{n}}=(a)^{\text{m}+\text{n}}\Big]$
$=5^o\times3^4=1\times81=81$ [$\because$ $a^0= 1$]
Solution:
Let $x$ be multiplied with $\Big(\frac{5}{3}\Big)^4$ to get $5^4$.
So,
$\Big(\frac{5}{3}\Big)^4\times\text{x}=5^4$
$\therefore$ $\text{x}=\frac{5^4}{\Big(\frac{5}{3}\Big)^4}$
$=5^4\times3^4\times5^{-4}=(5)^{4-4}\times3^4$ $\Big[\because\text{a}^{-\text{m}}=\frac{1}{\text{a}^\text{m}},\text{a}^\text{m}\times\text{a}^{\text{n}}=(a)^{\text{m}+\text{n}}\Big]$
$=5^o\times3^4=1\times81=81$ [$\because$ $a^0= 1$]
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