Question
Simplify and write the following in exponential form:
$\frac{9^8\times(\text{x}^2)^5}{(27)^4\times(\text{x}^3)^2}$
$\frac{9^8\times(\text{x}^2)^5}{(27)^4\times(\text{x}^3)^2}$
✓
Answer
$\frac{9^8\times(\text{x}^2)^5}{(27)^4\times(\text{x}^3)^2}$
$=\frac{(3^2)^8\times(\text{x}^2)^5}{(3^3)^4\times(\text{x}^3)^2}$
$=\frac{3^{16}\times\text{x}^{10}}{3^{12}\times\text{x}^6}$
$=3^{16-12}\times\text{x}^{10-6}$
$=3^4\times\text{x}^4$
$=(3\text{x})^{4}$
$=\frac{(3^2)^8\times(\text{x}^2)^5}{(3^3)^4\times(\text{x}^3)^2}$
$=\frac{3^{16}\times\text{x}^{10}}{3^{12}\times\text{x}^6}$
$=3^{16-12}\times\text{x}^{10-6}$
$=3^4\times\text{x}^4$
$=(3\text{x})^{4}$
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