Question Type 3: Rewriting expressions to apply exponents rules Exercises

Simplify $2^{-3} \times 4^2$ and express the result as $2^x$.

Simplify $(2^a)^3 \times 2^{2a}$ and express the result as $2^{ka}$, stating the value of $k$.

Find the value of $x$ given that $(3^2)^{-1} \times 9 = 3^x$.

Given that $\displaystyle\frac{\sqrt{x}\,x^{3/2}}{x^2} = x^p$, find the value of $p$.

Simplify $27^{2/3}\times9^{3/2}$ and express the result as $3^x$.

Simplify $\displaystyle\frac{2^4\times4^{-2}}{8^{-1}}$ and express the result as $2^x$.

Simplify $\displaystyle\frac{4^3}{2^6}$ and express the result as $2^x$.

Simplify $16^{\frac{3}{2}}$ and express the result as $2^x$.

Write $\displaystyle\left(\frac{8\cdot2^{20}}{2^{14}}\right)^{11}$ as $2^x$.

Express $2^5 \times 3^5$ as a single power.