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Exponent Operations Practice
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Exponent Operations Practice
Use the laws of exponents to simplify each expression. Show working where asked. Assume variables are non-zero where division is involved.
Laws of Exponents
1.Simplify 6³ × 6⁴.
- 6⁷
- 36⁷
- 6¹²
- 12⁷
2.Simplify 9⁸ ÷ 9³.
- 9¹¹
- 9⁵
- 3⁵
- 1⁵
3.Select every expression equal to 5⁶.
- 5² × 5⁴
- 5⁹ ÷ 5³
- 5⁸ ÷ 5²
- 5³ × 5³
4.Simplify 3 × 2⁴ × 2². Do not combine the 3 and 2 into a single power.
- 3 × 2⁶
- 6⁶
- 3 × 2⁸
- 3 × 4⁶
5.Match each expression to its simplified form.
- a⁴ × a³
- b⁹ ÷ b⁵
- x² × x × x⁵
- m⁶ ÷ m²
- x⁸
- a⁷
- m⁴
- b⁴
Show Your Working
6.Simplify 7⁵ ÷ 7², then evaluate the result. Show how the division law applies.
7.Simplify 4³ × 4² × 4⁴. Write the simplified power and its value.
8.Complete the simplification of (3⁴ × 3²) ÷ 3³. State the exponent after each law is used.
9.Estimate 2⁷ by using the known value 2⁶ = 64. Then calculate 2⁷ exactly and explain how the estimate helps check your result.
Apply and Explain
10.A lab sample contains 2⁴ cells. The sample doubles in size each hour. Write a power expression for the number of cells after 3 hours, then calculate the total.
11.In your own words, describe how to multiply two powers with the same base. Include a numerical example.
12.Simplify (8³ × 8⁵) ÷ 8⁴. Show each step and use the terms base and exponent in your explanation.
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