Question
Simplify:
$\frac{3}{5}^4\frac{8}{5}^{-12}\frac{32}{5}^6$
$\frac{3}{5}^4\frac{8}{5}^{-12}\frac{32}{5}^6$
✓
Answer
$\frac{3}{5}^4\frac{8}{5}^{-12}\frac{32}{5}^6=\frac{3^4}{5^4}\times\Big(\frac{5}{2^3}\Big)^{12}\times\Big(\frac{2^5}{5}\Big)^6\Big(\because\text{a}^{-1}=\frac{1}{\text{a}}\Big)$
$=\frac{3^4}{5^4}\times\frac{5^{12}}{2^{36}}\times\frac{2^{30}}{5^6}$ $[\because(\text{a}^\text{m})^\text{n}=\text{a}^\text{mn}]$
$=\frac{3^4\times5^{12-4-6}}{2^{36-30}}$ $[\because\frac{\text{a}^\text{m}}{\text{a}^\text{n}}=\text{a}^\text{m}-\text{n}]$
$=\frac{3^4}{2^6}\times5^2=\frac{81\times25}{64}=\frac{2025}{64}$
$=\frac{3^4}{5^4}\times\frac{5^{12}}{2^{36}}\times\frac{2^{30}}{5^6}$ $[\because(\text{a}^\text{m})^\text{n}=\text{a}^\text{mn}]$
$=\frac{3^4\times5^{12-4-6}}{2^{36-30}}$ $[\because\frac{\text{a}^\text{m}}{\text{a}^\text{n}}=\text{a}^\text{m}-\text{n}]$
$=\frac{3^4}{2^6}\times5^2=\frac{81\times25}{64}=\frac{2025}{64}$
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