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# Word Problems Involving Exponents Practice Questions

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Updated on Oct 4, 2011

To review these concepts, go to Word Problems Involving Exponents Study Guide.

## Word Problems Involving Exponents Practice Questions

### Practice 1

#### Problems

Simplify each of the following expressions.

1. 23× 25=
2. 23× 32=
3. x7× x6=
4. 7–2 =

#### Solutions

1. 23× 25= 23 + 5 = 28
2. 23× 32= 2 × 2 × 2 × 3 × 3 = 8 × 9 = 72
3. x7× x6= x7+ 6 = x13
4. = 54 – 3= 5

### Practice 2

#### Problems

Match the scientific notation with the correct standard form

 1. 4.3 × 10–3 a. 43 2. 4.3 × 103 b. 0.0000043 3. 4.3 × 10–6 c. 4,300 4. 4.3 × 10–1 d. 0.0043 5. 4.3 × 101 e. 0.43

#### Solutions

 1.4.3 × 10–3 d. 0.0043 2.4.3 × 103 c. 4,300 3.4.3 × 10–6 b. 0.0000043 4.4. 4.3 × 10–1 e. 0.43 5.4.3 × 101 a. 43

### Practice 3

#### Problems

1. What is the product of 43and 45?
2. What is the quotient of ?
3. What is the product of y12and y4?
4. What is the quotient of 75÷ 78?
5. The population of a country is written as 4.23 × 106people. What is the population expressed in standard form?
6. The diameter of a microscopic cell is 0.00056 cm. What is the diameter expressed in scientific notation?

#### Solutions

1. Read and understand the question. This question is looking for the product of two values that have the same base.
2. Make a plan. Add the exponents to find the solution.

Carry out the plan. The problem becomes 43× 45= 43 + 5= 48.

= 45

Because this was the other factor, this answer is checking.

3. Read and understand the question. This question is looking for the quotient of two values that have the same base.
4. Make a plan. Subtract the exponents to find the solution.

Carry out the plan. The problem becomes

= x7

x7× x3= x7 + 3
= x10

Because this was the first value given in the question, this answer is checking.

5. Read and understand the question. This question is looking for the product of two values that have the same base.
6. Make a plan. Add the exponents to find the solution.

Carry out the plan. The problem becomes

y12× y4= y12 + 4
= y16

= y4

Because this was the other factor, this answer is checking.

7. Read and understand the question. This question is looking for the quotient of two values that have the same base.
8. Make a plan. Subtract the exponents to find the solution.

Carry out the plan. The problem becomes

=7–3

=78–3
=75

Because this was the first value given in the question, this answer is checking.

9. Read and understand the question. This question is looking for the standard form when the number in scientific notation is given.
10. Make a plan. Use the value between one and 10 and move the decimal point the number of places given by the exponent. Use zeros as placeholders where necessary.

Carry out the plan. Take the decimal 4.23 and move the decimal point 6 places to the right. Add zeros as placeholders where necessary. The number becomes 4,230,000.

Check your answer. To check your answer, convert from standard form back to scientific notation. Place the decimal point between the 4 and the 2. Since the decimal point has moved six places to the left, the exponent of 10 will be 6. The scientific notation is 4.23 × 106, which was the value given in the question. This answer is checking.

11. Read and understand the question. This question is looking for the scientific notation when the standard form is given.
12. Make a plan. Form a number between one and 10, and then write this number multiplied by a power of 10. The exponent is the number of places the decimal point moves from the end of the number to between the 5 and the 6.

Carry out the plan.Write the decimal 5.6. Next, multiply this value by 10–4 because the decimal point moves 4 places to the right. The scientific notation is 5.6 ×10–4.

Check your answer. To check your answer, put this number back into standard form. Take the decimal 5.6 and move the decimal 4 places to the left. Add zeros as placeholders where necessary. The number becomes 0.00056. This answer is checking.

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