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What Are Powers?

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Powers Activities 1

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Powers Activities 2

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Addition and Subtraction of Powers

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Powers Activities 3

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The Multiplication Rule

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Powers Activities 4

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The Division Rule

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Powers Activities 5

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All Power Rules

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Powers Activities 6

6.1)

Simplify the expressions as much as possible:

a): $x^{8} \cdot y^{2} \cdot x^{4} \cdot x \cdot y$
b): $a \cdot b \cdot c \cdot a^{2} \cdot b^{3} \cdot c^{4}$
c): $6^{2} \cdot t^{3} \cdot 6 \cdot t^{- 1}$

6.2)

Simplify the expressions as much as possible:

a): ${(x \cdot y)}^{4}$
b): ${(8 x)}^{2}$
c): ${(2 x y)}^{2}$
d): ${(x y)}^{5} {(3 x)}^{3}$
e): ${(1 0^{3} x)}^{4}$
f): ${(a \cdot b^{2})}^{2} \cdot a^{4}$

a): ${(x \cdot y)}^{4}$
b): ${(8 x)}^{2}$
c): ${(2 x y)}^{2}$
d): ${(x y)}^{5} {(3 x)}^{3}$
e): ${(1 0^{3} x)}^{4}$
f): ${(a \cdot b^{2})}^{2} \cdot a^{4}$

6.3)

Simplify the expressions as much as possible:

a): ${(x^{3})}^{6}$
b): ${(2^{2})}^{2}$
c): ${(5 x^{3})}^{2}$
d): ${(2 a^{3})}^{5}$
e): $x^{2} \cdot x^{- 1}$

a): ${(x^{3})}^{6}$
b): ${(2^{2})}^{2}$
c): ${(5 x^{3})}^{2}$
d): ${(2 a^{3})}^{5}$
e): $x^{2} \cdot x^{- 1}$

6.4)

Calculate if possible or write as a single power:

a): $5^{- 6} \cdot 5^{8} \cdot 5^{- 2}$
b): ${(x^{- 2})}^{- 1}$
c): ${({(b^{2})}^{- 1})}^{- 2}$

6.5)

Simplify as much as possible:

a): ${(8 x y^{- 1})}^{- 2}$
b): $32 x \cdot {(2 x^{3})}^{- 4}$
c): ${(8 x y^{4})}^{- 2} \cdot {(4 x^{5})}^{2}$
d): ${(3 y^{6})}^{3} \cdot 10 x^{2} y^{12}$

a): ${(8 x y^{- 1})}^{- 2}$
b): $32 x \cdot {(2 x^{3})}^{- 4}$
c): ${(8 x y^{4})}^{- 2} \cdot {(4 x^{5})}^{2}$
d): ${(3 y^{6})}^{3} \cdot 10 x^{2} y^{12}$

6.6)

Simplify as much as possible:

a): $3^{n} \cdot 3^{n}$
b): $5^{n} \cdot 5^{1 - n} \cdot 5$
c): $4^{3} \cdot 4^{x}$

a): $3^{n} \cdot 3^{n}$
b): $5^{n} \cdot 5^{1 - n} \cdot 5$
c): $4^{3} \cdot 4^{x}$

You can find the solutions here.

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Example with Fractions

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Powers Activities 7

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Example with Roots

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Powers Activities 8

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Powers Activities 9

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Powers Solutions