Exponents Practice Questions

Use these Exponents practice questions to review scientific notation, exponent rules, negative exponents, powers of powers, and simplifying exponential expressions. After answering each question, open the explanation to see how the problem is solved step by step.

Exponents Topics Covered

  • Writing numbers in scientific notation
  • Converting scientific notation to standard notation
  • Multiplying expressions with the same base
  • Dividing expressions with the same base
  • Using the power rule for exponents
  • Simplifying expressions with negative exponents
  • Working with exponential expressions that include variables

Exponents Practice Questions

1. Write 0.000078 in scientific notation.

  1. 7.8 × 10−5
  2. 7.8 × 10−4
  3. 7.8 × 10−3
  4. 7.8 × 104
  5. 7.8 × 105
Show Answer

Answer: A. 7.8 × 10−5

Scientific notation uses a number between 1 and 10 multiplied by a power of 10.

Move the decimal point in 0.000078 until it is between the 7 and the 8:

0.000078 = 7.8

The decimal point moved 5 places to the right. Since the original number is less than 1, the exponent is negative.

So, 0.000078 = 7.8 × 10−5.

2. Multiply. Write the answer in exponential form.
46 × 43

  1. 42
  2. 48
  3. 49
  4. 412
  5. 418
Show Answer

Answer: C. 49

When multiplying exponential expressions with the same base, add the exponents.

46 × 43 = 46 + 3

46 + 3 = 49

3. Simplify the expression.


(

a2b
ab3

)3

  1. a6b6
  2. a3b6
  3. a3b−6

  4. b6
    a3

  5. a3
    b6
Show Answer


Answer: E.

a3
b6

First simplify inside the parentheses.



a2b
ab3

=

a
b2

Now raise both the numerator and denominator to the third power.


(

a
b2

)3
=

a3
b6

4. Simplify the expression.


x2
x−4

  1. x−6
  2. x−2
  3. x2
  4. x6
  5. x8
Show Answer

Answer: D. x6

When dividing expressions with the same base, subtract the exponents.

x2 ÷ x−4 = x2 − (−4)

Subtracting a negative number is the same as adding.

x2 − (−4) = x6

5. Write 8,000,000 in scientific notation.

  1. 8 × 104
  2. 8 × 105
  3. 8 × 106
  4. 80 × 104
  5. 80 × 105
Show Answer

Answer: C. 8 × 106

Scientific notation uses a number between 1 and 10 multiplied by a power of 10.

Move the decimal point in 8,000,000 until it is after the 8.

8,000,000 = 8.0

The decimal point moved 6 places to the left, so the exponent is positive 6.

Therefore, 8,000,000 = 8 × 106.

6. Divide.
4y6 ÷ 0.5y−3

  1. 2y2
  2. 2y9
  3. 8y2
  4. 8y9
  5. 8y18
Show Answer

Answer: D. 8y9

First divide the coefficients.

4 ÷ 0.5 = 8

Then divide the exponential terms by subtracting the exponents.

y6 ÷ y−3 = y6 − (−3)

y6 − (−3) = y9

So the simplified expression is 8y9.

7. Write in standard notation.
2.84 × 104

  1. 0.000284
  2. 0.00284
  3. 2.840000
  4. 2,840
  5. 28,400
Show Answer

Answer: E. 28,400

The exponent is positive 4, so move the decimal point 4 places to the right.

2.84 × 104 = 28,400

8. Simplify the expression.


(a2)3
a−6

  1. a−12
  2. a−7
  3. a
  4. a7
  5. a12
Show Answer

Answer: E. a12

First use the power rule. When raising a power to another power, multiply the exponents.

(a2)3 = a6

Now divide the exponential terms by subtracting the exponents.

a6 ÷ a−6 = a6 − (−6)

a6 − (−6) = a12

9. Simplify the expression.
(3x4)3

  1. 3x7
  2. 3x12
  3. 9x7
  4. 9x12
  5. 27x12
Show Answer

Answer: E. 27x12

Apply the exponent to both the coefficient and the variable.

(3x4)3 = 33(x4)3

33 = 27

(x4)3 = x12

So the simplified expression is 27x12.

10. Divide.


12a8
3a2

  1. 3a4
  2. 3a6
  3. 4a4
  4. 4a6
  5. 9a4
Show Answer

Answer: D. 4a6

Divide the coefficients first.

12 ÷ 3 = 4

Then divide the exponential terms by subtracting the exponents.

a8 ÷ a2 = a8 − 2

a8 − 2 = a6

So the simplified expression is 4a6.

How to Use These Exponents Practice Questions

Start by answering each question before opening the explanation. Then compare your work to the step-by-step solution. If you miss a question, review the exponent rule involved before moving on.

For extra review, focus on the types of questions you missed most often. Scientific notation, product rules, quotient rules, negative exponents, and powers of powers show up frequently, so strengthening those skills can make exponent problems easier to handle.

 

Last Updated: July 9, 2026