Advanced problem solving with the laws of indices

12 questions

1. Evaluate 16^\frac{1}{2}, giving the positive solution where necessary.
2. Evaluate 9^\frac{3}{2}, giving the positive solution where necessary.
3. Evaluate 25^\frac{1}{2}, giving the positive solution where necessary.
4. What is the value of b for b^7 \div b^5 =9^2?
5. What is the value of k for 0.2^5 \div 0.2^k = 0.2^7?
6. What number is written as 2^3 \times 5 \times 7 as a product of its prime factors?
7. What is the value of x for (3^3)^4 × 3^2 = 3^x ?
8. What is the value of x for \frac{2^{12} \times 2^4}{2^{10}} = 2^x ?
9. What is the value of x for \frac{5^{14} \times 5^5}{5^{-2}} = 5^x ?
10. What is the value of x for 3^2 \times 3^6 = 9^x ?
11. What is the value of x for 2^3 \times 4^3 = 2^x ?
12. What is the value of x^{4x} for 2^x \times 2^{3x} = x^{4x} ?

License: OGL