SIMPLIFYING EXPONENTIAL EXPRESSIONS WORKSHEET

Simplify : 

1)  a⁴ ⋅ b⁵ ⋅ a²

2)  x² ⋅ x ⋅ x^-4

3)  (y²)^-4 ⋅ y⁵

4)  (xy²)^-4 ⋅ (x³y⁵)²

5)  (-5x)²

6)  -(5x)²

7)  (a^-2 ⋅ b⁰)³

8)  xy³/y⁵

9)  x⁵y⁹/(xy)⁴

10)  (2a³/bc)³

11)  (3a/b²)^-3

12)  (3/4)^-1 ⋅ (2a/3b)^-2

Detailed Answer Key

Answer (1) :

=  a⁴ ⋅ b⁵ ⋅ a²

Group powers with the same base together. 

=  (a⁴ ⋅ a²) ⋅ b⁵

Add the exponents of powers with the same base.   

=  a^{4 + 2} ⋅ b⁵

=  a⁶ ⋅ b⁵

Answer (2) :

=  x² ⋅ x ⋅ x^-4

Because the powers have the same base, keep the base and add the exponents.  

=  x^{2 + 1 + (-4)}

=  x^{2 + 1 - 4}

=  x^-1

=  1/x

Answer (3) :

=  (y²)^-4 ⋅ y⁵

Use the Power of a Power Property. 

=  y^-8 ⋅ y⁵

=  y^{-8 + 5}

=  y^-3

=  1/y³

Answer (4) :

=  (xy²)^-4 ⋅ (x³y⁵)²

Use the Power of a Power Property. 

=  x^-4(y²)^-4 ⋅ (x³)²(y⁵)²

=  x^-4y^-8 ⋅ x⁶y¹⁰

Group powers with the same base together. 

=  (x^-4 ⋅ x⁶) ⋅ (y^-8 ⋅ y¹⁰)

=  x^{-4 + 6} ⋅ y^{-8 + 10}

=  x²y²

Answer (5) :

=  (-5x)²

Use the Power of a Product Property. 

=  (-5)² ⋅ x²

=  25x²

Answer (6) :

=  -(5x)²

Use the Power of a Product Property. 

=  -(5² ⋅ x²)

=  -(25 ⋅ x²)

=  -25x²

Answer (7) :

=  (a^-2 ⋅ b⁰)³

Use the Power of a Product Property. 

=  (a^-2)³ ⋅ (b⁰)³

=  a^-2 ⋅ 3 ⋅ b^0 ⋅ 3

=  a^-6 ⋅ b⁰

=  x^-6 ⋅ 1

=  1/a⁶

Answer (8) :

=  xy³/y⁵

Use the Quotient of Powers Property. 

=  xy^{3 - 5}

=  xy^-2

=  x/y²

Answer (9) :

=  x⁵y⁹/(xy)⁴

Use the Power of a Product Property. 

=  x⁵y⁹/x⁴y⁴

Use the Quotient of Powers Property. 

=  x^5-4 ⋅ y^9-4

=  x¹ ⋅ y⁵

=  xy⁵

Answer (10) :

=  (2a³/bc)³

Use the Power of a Quotient Property. 

=  (2a³)³/(bc)³

Use the Power of a Power Property. 

=  2³(a³)³/(b³c³)

=  8a⁹/b³c³

Answer (11) :

=  (3a/b²)^-3

Rewrite with a positive exponent. 

=  (b²/3a)³

Use the Power of a Quotient Property. 

=  (b²)³/(3a)³

Use the Power of a Power Property. 

=  b⁶/(3³a³)

=  b⁶/27a³

Answer (12) :

=  (3/4)^-1 ⋅ (2a/3b)^-2

Rewrite each fraction with a positive exponent. 

=  (4/3)¹ ⋅ (3b/2a)²

Use the Power of a Quotient Property. 

=  (4/3) ⋅ (3b)²/(2a)²

Use the Power of a Power Property. 

=  (4/3) ⋅ (3²b²/2²a²)

=  (4/3) ⋅ (9b²/4a²)

Simplify. 

=  3b²/a²

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