Worksheets - Week 2 - Exponent Rules PDF

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Worksheet 1 – Exponent Rules (Multiplication) Simplify the following expressions, showing all steps demonstrated in the example below.

Example (2𝑥 )(−3𝑥 2 ) = 2(−3) ∙ 𝑥 ∙ 𝑥 2 = −6𝑥 3 1) (3𝑥)(−4𝑥 3 )

2) 2 ∙ 3𝑥 ∙ 4𝑥 2

3) (−2𝑥𝑦)(𝑥 2 𝑦 2 )

4) 𝑥 ∙ 𝑦 ∙ 𝑦 ∙ 𝑥 ∙ 𝑥

5) 2(𝑥 3 𝑦 2 )(3𝑥)

6) 3𝑥𝑦 ∙ 2𝑥 ∙ 3𝑦 2

7) (8𝑥 2 )(−2𝑥𝑦)

8) (−𝑎𝑏𝑐 2 )(𝑎𝑏)

9) 3 ∙ 4𝑥 ∙ (−3𝑥𝑦)

10) (3𝑎2 ) ∙ 2𝑎𝑏 2

11) −7𝑥 2 𝑦 3 𝑥 2 𝑦 2

12) (4𝑥 2 𝑦 3 )(−𝑥𝑦)

13) (2𝑥𝑦)(𝑧𝑦𝑥)(−𝑥𝑦𝑧)

14) (−𝑥)(𝑥)(−𝑦)(−𝑥𝑦)

[1]

Worksheet 2 – Exponent Rules (Dividing) Simplify the following expressions, showing all steps demonstrated in the example below.

Example 3𝑥 2 𝑦 3𝑥 2 9𝑥 6 𝑦

=

3𝑥 4 𝑦 3 9𝑥 6 𝑦

=

3 𝑥4 ( 9 ∙ 𝑥6

∙

𝑦3 𝑦

=) =

−2𝑥 2 𝑦 1) 4𝑥𝑦 2

3)

−8𝑥𝑦

5)

2𝑥∙(−2𝑥)

3𝑥 2 𝑥3 2) 2𝑥𝑦

4)

2𝑥 2 𝑦

6)

𝑥𝑦

4𝑥 2 𝑦𝑥 7) 6𝑥𝑦

9)

𝑦2

𝑥 2𝑦3 −2𝑥𝑦 3

−3𝑥𝑦 2 −5𝑦

4𝑥 2 ∙2𝑥 2 8) 2𝑥∙𝑥𝑦

(8𝑥 2 )(2𝑥)

10)

2𝑥

[2]

2𝑥

3𝑥𝑦

Worksheet 3 – Exponent Rules (Mixed Problems) Simplify the following expressions, showing all steps

3𝑥 2 𝑦

1) 𝑥 −2

2)

3) 2𝑥 −2

4) 2𝑥 0 𝑦 3 (3𝑥𝑦 2 )

5) (2𝑥)−2

6)

[3]

𝑥 −1 𝑦

𝑥 2 𝑦 −1 2𝑥 3 𝑦

7) (−3𝑥 2 𝑦)2

(2𝑎)−1 (2𝑏2 ) 8) 2𝑎0 𝑏

9) (2𝑥 )0 (4𝑥)3

10) (4𝑥 2 𝑦)(−2𝑥𝑦)

11)

(2𝑎)(2𝑏 2 )

12)

2𝑎0 𝑏

[4]

4𝑎3 𝑏 2 2𝑎𝑏4...