Question
$\frac{125\times\text{x}^{-3}}{5^{-3}\times25\times\text{x}^{-6}}$
✓
Answer
Using laws of exponents, $a^m÷ a^n= (a)^{n-m}$ and $\text{a}^{-\text{m}}=\frac{1}{\text{a}^{\text{m}}}$
$\therefore \frac{125\times\text{x}^{-3}}{5^{-3}\times25\times\text{x}^{-6}}$
$=(5)^3\times5^3\times5^{-2}\times\text{x}^{-3}\times\text{x}^6$ [$\because 125 = 5 \times 5 \times 5$ and $25 = 5 \times 5]$
$=5^4\times\text{x}^3$
$=5\times5\times5\times5\times\text{x}^3$
$=625\text{x}^3$ [$\because$
$a^m\times a^n= a^{m+n}]$
$\therefore \frac{125\times\text{x}^{-3}}{5^{-3}\times25\times\text{x}^{-6}}$
$=(5)^3\times5^3\times5^{-2}\times\text{x}^{-3}\times\text{x}^6$ [$\because 125 = 5 \times 5 \times 5$ and $25 = 5 \times 5]$
$=5^4\times\text{x}^3$
$=5\times5\times5\times5\times\text{x}^3$
$=625\text{x}^3$ [$\because$
$a^m\times a^n= a^{m+n}]$
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