The laws of indices - fractional exponents

12 questions

1. What is the value of x for (m^x)^8 = m^{32}
2. What is the value of x for (m^{-2})^5 = m^x
3. What is the value of x for (m^8)^x = m^{80}
4. What is the value of x for \frac{1}{16} = 2^x
5. What is the value of x for \frac{1}{64} = x^{-6}
6. What is the value of a for 7^9 \times 7^a = 7^6?
7. Evaluate 36^{\frac{1}{2}}, giving the positive solution where necessary.
8. Evaluate 1000^{\frac{1}{3}}, giving the positive solution where necessary.
9. Evaluate 27^{\frac{2}{3}}, giving the positive solution where necessary.
10. Evaluate 1000^{\frac{2}{3}}, giving the positive solution where necessary.
11. Evaluate 16^{\frac{3}{4}}, giving the positive solution where necessary.
12. Evaluate 16^{\frac{3}{2}}, giving the positive solution where necessary.

License: OGL