Question

Express the following in exponential form , using laws :

$\frac{{\left(x^{-2}\right)}^3\times {\left(y^2\right)}^3\times {\left(z^2\right)}^{-3}\times {\left(5^2\right)}^3}{{\left(2x^2\right)}^3\times {\left(y^{-3}\right)}^2\times {\left(-5\right)}^3}$

Answer 1

Given that , $\frac{{\left(x^{-2}\right)}^3\times {\left(y^2\right)}^3\times {\left(z^2\right)}^{-3}\times {\left(5^2\right)}^3}{{\left(2x^2\right)}^3\times {\left(y^{-3}\right)}^2\times {\left(-5\right)}^3}$

$=\frac{x^{-2\times 3}\times y^{2\times 3}\times z^{-3\times 2}\times 5^{2\times 3}}{2^3{x}^{2\times 3}\times y^{-3\times 2}\times {\left(-1\right)}^3\times {\left(5\right)}^3}$

$=\frac{x^{-6}\times y^6\times z^{-6}\times 5^6}{2^3\times x^6\times y^{-6}\times -1\times 5^3}$

$=\frac{1}{2^3}{x}^{-6-6}\times y^{6+6}\times z^{-6}\times 5^{6-3}\times \left(-1\right)$

$=-\frac{5^3}{2^3}\times x^{-12}\times y^{12}\times z^{-6}$

Hence, the required value is $-\frac{5^3}{2^3}\times x^{-12}\times y^{12}\times z^{-6}$ .