Quiz: Exponents Practice Questions (set 1)

This quiz contains questions designed to test your understanding of the fundamentals of exponents, as explained in the video on this page. While these questions are primarily intended for middle school students, anyone is welcome to take the quiz to assess their understanding of exponents. Please refrain from using external resources to assist in solving the questions. If your answers are incorrect, feel free to retake the quiz and try to get them all right. If you notice any errors in the questions or answers, please leave a comment. Enjoy the quiz!

1. 
If $2^x = 32$, find the value of $x$.

2. 
Simplify: $( x^3 \cdot y^2 )^2$.

3. 
Solve for $x$: $2^{2x} = 16$.

4. 
Simplify: $\frac{(3^2)^4}{3^6}$.

5. 
Simplify: $x^{1/2} \cdot x^{1/3}$.

6. 
Solve for $x$: $3^{x + 1} − 3^x = 54$.

7. 
Solve for $x$: $5^{2x} = 125^{x-1}$.

8. 
Simplify: $(x^3 y^{-2})^{-4} \cdot x^{-6} y^8$.

9. 
Simplify: $(\frac{2x^3}{y^{-2}})^4$.

10. 
Solve for $x$: $3^{x+3} = 81^{x-2}$.

11. 
Simplify: $\frac{2^{2x} \cdot 4^{x+1}}{8^x}$.

12. 
Solve for $x$: $4^{x+2} = 2^{2x+5}$.

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