Laws of Exponents

Simplify: ${\left(5^{-1}-4^{-1}\right)}^{-1}+{\left(2^{-1}-3^{-1}\right)}^{-1}$

Simplify: ${\left[7^{-1}+{\left(\frac{3}{2}\right)}^{-1}\right]}^{-1}$

Simplify: ${\left[{\left\{{\left(-\frac{1}{3}\right)}^2\right\}}^{-2}\right]}^{-1}$

Simplify: $\frac{{\left(2^5\right)}^3\times 7^3}{8^3\times 7}.$

Find the value of $x$ in ${\left(\frac{1}{5}\right)}^{-3}\times {\left(\frac{1}{5}\right)}^{-5} = {\left(\frac{1}{5}\right)}^x$

Find the value of $x$ in ${\left(\frac{2}{7}\right)}^{-3}\times {\left(\frac{2}{7}\right)}^{-11} = {\left(\frac{2}{7}\right)}^{7x}$

Simplify: $\frac{3^6\times a^5}{9^2\times a^3}$

Simplify: $\frac{4\times 3^4\times 2^4}{2\times 2^5}$

Simplify: $\left[{\left(5^2\right)}^3\times 5^4\right]÷5^7$

Simplify: $\frac{3^5\times {10}^5\times 25}{5^7\times 6^5}.$

Simplify: $\left(\frac{2^7}{2^3}\right)\times 2^5$

Simplify: $(3^{20}÷3^{15})\times 3^3$

Simplify: $\frac{5^8}{5^5\times 5^3}$

Simplify: $\frac{25\times 5^2\times x^8}{{10}^3\times x^5}$

Simplify: $(2^3\times 2{)}^2$

Write $8\times 8\times 8$ in exponential form taking base as $2$.

Write $9\times 9\times 9\times 9$ in exponential form taking base as $3$

If ${\left(-7\right)}^{-1}$ is multiplied by a number, the product obtained is ${\left(\frac{6}{7}\right)}^{-1}$. What is the number?

Express $\frac{1}{6561}$ in exponential form

Evaluate: $\frac{2^{\mathrm{x}+3}\times 3^{2\mathrm{x}-\mathrm{y}}\times 5^{\mathrm{x}+\mathrm{y}+3}\times 6^{\mathrm{y}+1}}{6^{\mathrm{x}+1}\times {10}^{\mathrm{y}+3}\times {15}^{\mathrm{x}}}$