EXPONENTS

1. Simplify: \( 2^3 \times 2^5 \)
2. Evaluate: \( (3^2)^4 \)
3. Simplify: \( \frac{5^7}{5^3} \)
4. Express \( 8 \) as a power of \( 2 \)
5. Solve for \( x \): \( 2^x = 16 \)
6. Write \( \frac{1}{27} \) as a power of \( 3 \)
7. If \( 3^x = 81 \), find \( x \)
8. Evaluate: \( 10^0 + 10^{-1} \)
9. Simplify: \( (x^2y^3)^2 \)
10. Find the value of \( x \) in \( 5^x = \frac{1}{125} \)
11. Solve the equation: \( 4^x = 64 \)
12. Express \( 0.0001 \) as a power of \( 10 \)
13. Evaluate: \( (2^{-3})^2 \)
14. Simplify: \( \frac{x^{-2}}{x^3} \)
15. Find the value of \( x \) in \( 9^x = 1 \)
16. Simplify: \( 3x^2 \times 4x^3 \)
17. Solve: \( 2^{x+1} = 16 \)
18. Simplify: \( (ab^2)^3 \)
19. Solve: \( 10^{2x} = 100 \)
20. Find the value of \( x \): \( 2^x + 2^{x+1} = 48 \)
21. A population of bacteria doubles every hour. If there are 500 bacteria now, how many will there be in 5 hours?
22. The value of a car depreciates by half every year. If the car is worth $20,000 now, what will it be worth in 3 years?
23. A tree grows such that its height (in cm) doubles every 2 months. If the initial height is 10 cm, find the height after 8 months.
24. A machine increases production by a factor of 3 every day. If it produces 2 units today, how many units will it produce after 4 days?
25. In a video game, a player's score triples every round. If the starting score is 50, what is the score after 3 rounds?
26. The brightness of a star follows the rule \( B = 2^n \), where \( n \) is the number of magnitudes. Find the brightness when \( n = 6 \).
27. A loan grows by 5% interest compounded annually. If the initial amount is $1,000, express the amount after \( t \) years as an exponential expression.
28. Each page in a viral thread has 2 times the views of the previous. If the first page has 100 views, how many views does the 6th page have?
29. A radioactive substance halves in mass every hour. If the original mass is 80g, how much remains after 3 hours?
30. John earns TZS 4.2 on day one, and each day he earns double the previous day. How much will he earn on day 7?

RATIONALIZING THE DENOMINATORS REVISION QUESTIONS

Answers

1. \( 2^8 = 256 \)
2. \( 3^8 = 6561 \)
3. \( 5^4 = 625 \)
4. \( 2^3 \)
5. \( x = 4 \)
6. \( 3^{-3} \)
7. \( x = 4 \)
8. \( 1 + 0.1 = 1.1 \)
9. \( x^4y^6 \)
10. \( x = -3 \)
11. \( x = 3 \), since \( 4^3 = 64 \)
12. \( 10^{-4} \)
13. \( 2^{-6} = \frac{1}{64} \)
14. \( x^{-5} \)
15. \( x = 0 \), since \( 9^0 = 1 \)
16. \( 12x^5 \)
17. \( x+1 = 4 \Rightarrow x = 3 \)
18. \( a^3b^6 \)
19. \( x = 1 \)
20. \( 2^x + 2^{x+1} = 48 \Rightarrow 2^x(1+2) = 48 \Rightarrow 2^x = 16 \Rightarrow x = 4 \)
21. \( 500 \times 2^5 = 16000 \) bacteria
22. \( 20000 \times \left(\frac{1}{2}\right)^3 = 2500 \) dollars
23. \( 10 \times 2^4 = 160 \) cm
24. \( 2 \times 3^4 = 162 \) units
25. \( 50 \times 3^3 = 1350 \)
26. \( 2^6 = 64 \)
27. \( A = 1000(1.05)^t \)
28. \( 100 \times 2^5 = 3200 \) views
29. \( 80 \times \left(\frac{1}{2}\right)^3 = 10 \)g
30. \( 4.2(2)^6 = 268.8 \) TZS