Laws of indices Quiz

1. Simplify $\dfrac{6x^{7}}{2x^{-3}}$.

• A. $3x^{4}$
• B. $3x^{10}$
• C. $4x^{4}$
• D. $3x^{-21}$

2. Evaluate $16^{\frac34}$.

• A. $6$
• B. $12$
• C. $4$
• D. $8$

3. Evaluate $\left(\dfrac{1}{125}\right)^{-\frac23}$.

• A. $25$
• B. $\frac1{25}$
• C. $-25$
• D. $\frac{1}{5}$

4. Write $\dfrac{x^2}{\sqrt[3]{x}}$ as a single power of $x$ ($x>0$).

• A. $x^{\frac23}$
• B. $x^{\frac73}$
• C. $x^{\frac53}$
• D. $x^{6}$

5. Solve $x^{\frac23}=9$ for $x>0$.

• A. $x=6$
• B. $x=\sqrt{27}$
• C. $x=81$
• D. $x=27$