Worksheets: powers with rational basesgrades 7-8

Quizzes in groups and practice sheets on “Powers with rational bases” - with an answer key, ready to print, free. You can combine this section with topics from other sections.

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Answer key · group A · for the teacher · sheet no. 204 517

Powers with rational bases

1.1081 = 3⁴ ;81³ = (3⁴)³ = 3¹² ;3¹² : 3² = 3¹⁰ ;12 − 2 = 10

2.690 0006.9 · 10⁵ = 6.9 · 100 000 = 690 000

3.30 000(6 · 10⁻⁴) : (2 · 10⁻⁸) = 3 · 10⁴ ;6 : 2 = 3, −4 − (−8) = 4 ;3 · 10⁴ = 30000

4.169 + 6 − 13 = 2 ;(4⁹ · 4⁶) : 4¹³ = 4² ;4² = 16

5.305 · 6 = 30

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Answer key

Quiz

Powers with rational bases

GroupAB

Name Date Score / 16

1.Fill in the exponent:125³ · 5² : 25⁴ = 5☐(3 pt)

2.Write the number without a power:4.4 · 10³(2 pt)

3.Calculate and choose the result written in scientific notation:(1.5 · 10⁻⁷) : (6 · 10³)(3 pt)

A.2.5 · 10⁻⁵B.2.5 · 10⁻¹¹C.0.25 · 10⁻¹⁰D.2.5 · 10⁻¹⁰

4.Calculate:1.5¹¹ : 1.5¹⁰ · 1.5(2 pt)

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Group B

Quiz

Powers with rational bases

GroupAB

Name Date Score / 16

1.Fill in the exponent:81³ : 3² = 3☐(3 pt)

2.Write the number without a power:6.9 · 10⁵(2 pt)

3.How many times greater is the number 6 · 10⁻⁴ than the number 2 · 10⁻⁸?(3 pt)

4.Calculate:(4⁹ · 4⁶) : 4¹³(2 pt)

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Group A

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Quiz6 questions2 groups1 topic

Sheet no.204 517The number is only shown here and on the answer key - never on the student sheet. The same number with the same topics gives the same sheet.

answer key at the endall groups

Quiz

Powers with rational bases

GroupAB

Name Date Score / 16

1.Fill in the exponent:81³ : 3² = 3☐(3 pt)

2.Write the number without a power:6.9 · 10⁵(2 pt)

3.How many times greater is the number 6 · 10⁻⁴ than the number 2 · 10⁻⁸?(3 pt)

4.Calculate:(4⁹ · 4⁶) : 4¹³(2 pt)

5.Fill in the exponent:(8⁵)⁶ = 8☐(3 pt)

6.Choose the correct form.Write 0.00000831 in scientific notation.(3 pt)

A.8.31 · 10⁻⁵B.8.31 · 10⁻⁶C.83.1 · 10⁻⁷D.8.31 · 10⁶

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Answer key · group A · for the teacher · sheet no. 204 517

Powers with rational bases

1.1081 = 3⁴ ;81³ = (3⁴)³ = 3¹² ;3¹² : 3² = 3¹⁰ ;12 − 2 = 10

2.690 0006.9 · 10⁵ = 6.9 · 100 000 = 690 000

3.30 000(6 · 10⁻⁴) : (2 · 10⁻⁸) = 3 · 10⁴ ;6 : 2 = 3, −4 − (−8) = 4 ;3 · 10⁴ = 30000

4.169 + 6 − 13 = 2 ;(4⁹ · 4⁶) : 4¹³ = 4² ;4² = 16

5.305 · 6 = 30

6.B. 8.31 · 10⁻⁶0.00000831 · 10⁶ = 8.31 ;0.00000831 = 8.31 : 10⁶ = 8.31 · 10⁻⁶

The method lists the solution steps - handy when going through the sheet with the class.

Maths worksheets · phiboard.comsheet no. 999 999 · answer key, page 10 of 10

Quiz

Powers with rational bases

GroupAB

Name Date Score / 16

1.Fill in the exponent:125³ · 5² : 25⁴ = 5☐(3 pt)

2.Write the number without a power:4.4 · 10³(2 pt)

3.Calculate and choose the result written in scientific notation:(1.5 · 10⁻⁷) : (6 · 10³)(3 pt)

A.2.5 · 10⁻⁵B.2.5 · 10⁻¹¹C.0.25 · 10⁻¹⁰D.2.5 · 10⁻¹⁰

4.Calculate:1.5¹¹ : 1.5¹⁰ · 1.5(2 pt)

5.Fill in the exponent:(5⁸)² = 5☐(3 pt)

6.Write the number as a decimal:6.02 · 10⁻⁵(3 pt)

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Answer key · group B · for the teacher · sheet no. 204 517

Powers with rational bases

1.3125 = 5³, 25 = 5² ;125³ = (5³)³ = 5⁹, 25⁴ = (5²)⁴ = 5⁸ ;5⁹ · 5² : 5⁸ = 5³ ;9 + 2 − 8 = 3

2.44004.4 · 10³ = 4.4 · 1000 = 4400

3.B. 2.5 · 10⁻¹¹1.5 : 6 = 0.25, −7 − 3 = −10 ;0.25 · 10⁻¹⁰ = 2.5 · 10⁻¹¹ ;(1.5 · 10⁻⁷) : (6 · 10³) = 2.5 · 10⁻¹¹

4.2.2511 − 10 + 1 = 2 ;1.5¹¹ : 1.5¹⁰ · 1.5 = 1.5² ;1.5² = 2.25

5.168 · 2 = 16

6.0.00006026.02 · 10⁻⁵ = 6.02 : 10⁵ = 0.0000602

The method lists the solution steps - handy when going through the sheet with the class.

Maths worksheets · phiboard.comsheet no. 999 999 · answer key, page 10 of 10

Worksheets from this section

Every topic has its own page with a printable sheet.

What the section covers in the curriculum: powers with natural exponents, multiplying and dividing powers, power of a power, scientific notation for large and small numbers, calculating in scientific notation

Powers with natural exponentsQuiz · practice sheet Multiplying and dividing powersQuiz · practice sheet Power of a powerQuiz · practice sheet Scientific notationQuiz · practice sheet Small numbers and calculations in scientific notationQuiz · practice sheet

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