Mastering Exponents: Evaluating and Converting Forms

1. If 2^x = 32, what is the value of x?

• 6

• 8

• 5

• 4

2. A bacteria culture doubles every 3 hours. If there are initially 100 bacteria, how many will there be after 12 hours?

• 1600

• 3200

• 400

• 800

3. Simplify the expression (3^4) * (3^2) and provide the final answer in exponential form.

• 3^5

• 3^4

• 3^8

• 3^6

4. Convert the expression 5^3 * 5^2 into a single exponent and evaluate it.

• 3125

• 625

• 1000

• 125

5. If 4^x = 64, what is the value of x?

• 2

• 3

• 4

• 5

6. A car's value decreases by half every year. If the car is worth $16,000 now, what will its value be in 3 years?

• $2,000

• $8,000

• $1,000

• $4,000

7. Simplify the expression (2^5)/(2^2) and provide the answer in exponential form.

• 2^1

• 2^2

• 2^5

• 2^3

8. If 10^x = 0.01, what is the value of x?

• -2

• 0

• -1

• 2

9. A computer's processing speed is measured in gigahertz (GHz) and is represented as 2^3 GHz. What is the speed in standard form?

• 16 GHz

• 2 GHz

• 8 GHz

• 4 GHz

10. If a tree grows at a rate of 2^n cm per year, how tall will it be after 5 years if it starts at 10 cm?

• 30 cm

• 100 cm

• 72 cm

• 50 cm