IB Mathematics Applications & Interpretation Question Type 3: Rewriting Expressions to Apply Exponent Rules Exercises

Find the value of $n$ such that $\frac{9^{3/2}}{3}=3^n$.

Simplify $(3^4\cdot 3^{-2}{)}^3$ and write the result as $3^n$.

Express $(16\cdot 2^{-3}{)}^{-2}$ as $2^n$.

Express $27^{2/3}\cdot 9^{1/2}$ as $3^n$.

Simplify ${\left(\frac{81}{3^4}\right)}^{-1}$ and express it in the form $3^n$.

Express ${\left(\frac{32}{2^3}\right)}^4$ as $2^n$.

Express $\frac{2^5\cdot 4^{-2}\cdot 8^3}{16}$ as $2^n$.

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

Simplify $(x^{\frac{1}{2}}\cdot x^{\frac{3}{4}}{)}^2$ and write the result as $x^n$.

Simplify $\frac{7^0\cdot 7^5}{7^2}$ and write the answer as $7^n$.

Find the value of $n$ such that $5^3\cdot 25^2=5^n$.

Simplify $\frac{4^5}{8^2}$ and express your answer as $2^n$.