Question

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Answer 1

Answer↷

$\frac{ {9}^{8} \times ( {x}^{2} ) {}^{5} }{(27) {}^{4} \times ( {x}^{3} ) {}^{2} } \\ \\ \frac{ {9}^{8} \times {x}^{10} }{(3 {}^{3} ) {}^{4} \times {x}^{6} } \\ \\ \frac{ {9}^{8} \times {x}^{10} }{3 {}^{12 } \times {x}^{6} } \\ \\ \frac{3 {}^{16} \times {x}^{10} }{ {3}^{12} \times {x}^{6} } \\ \\ \green{ \implies {3}^{4} \times {x}^{4} } \ \ \green{= (3x) {}^{4} }$

Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

To simplify:

• $\dfrac{9^8\times(x^2)^5}{27^4\times(x^3)^2}$

Solution:

$\dfrac{9^8\times (x^2)^5}{27^4\times (x^3)^2}\\\\\implies \dfrac{(3^2)^8\times (x^2)^5}{(3^3)^4\times (x^3)^2} \\\\\implies \dfrac{3^{16}\times x^{10}}{3^{12}\times x^{6}} \\\\\implies 3^{16-12} \times x^{10-6} \\\\\implies 3^4 \times x^4 \\\\\implies\bf{(3x)^4} \\\\\implies \bf{81x^4}$

Learn More:

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$