IB Mathematics Analysis and Approaches 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 $\frac{\sqrt{x}{x}^{3/2}}{x^2}=x^p$, find the value of $p$.

Simplify $27^{2/3}\times 9^{3/2}$ and express the result as $3^x$.

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

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

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

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

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