Question Type 3: Rewriting expressions to apply exponent rules Exercises

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

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

Express $(16\cdot2^{-3})^{-2}$ 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 $\displaystyle\frac{2^5 \cdot 4^{-2} \cdot 8^3}{16}$ as $2^n$.

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

Simplify $(x^{\tfrac{1}{2}}\cdot x^{\tfrac{3}{4}})^2$ 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 $2^n$.