**Apply exponent properties involving products worksheets**** :**

Apply exponent properties involving products worksheets are much useful to the students who would like to practice problems on exponent properties.

(1) Simplify (5x²)⁴ x (2x)³

(2) If 5 √5 x 5³= 5 ⁽ⁿ⁺²⁾ then find the value of n.

(3) Simplify (52 x⁶/13x⁻⁷)

(4) Simplify (-7x²) (x⁴)

(5) Simplify (10 x y³ z²) (-2 x y⁵z)

(6) Simplify (-5 xyz) (4 y⁵z) y³

(7) Simplify (7 a b² c³) (¾ a b c⁴)

(8) Simplify (-4 a³) (-5 a⁴)

(9) Simplify (2 a³) (¼) a⁴

(10) Simplify (10 p³) (7/25) p⁷

**Question 1 :**

Simplify (5x²)⁴ x (2x)³

**Solution :**

= (5x²)⁴ x (2x)³

5⁴ = 5 x 5 x 5 x 5

2³ = 2 x 2 x 2

Since x⁸ and x³ are having same base, we can combine these terms.

**Question 2 :**

If 5 √5 x 5³= 5 ⁽ⁿ⁺²⁾ then find the value of n.

**Solution :**

**Question 3 :**

Simplify (52 x⁶/13x⁻⁷)

**Solution :**

= (52 x⁶/13x⁻⁷)

We have negative power for the x term which is in the denominator.To make it as positive we are going to write it in numerator.

= (52 x⁶x⁷/13)

= 4 x⁽⁶⁺⁷⁾

= 4 x¹³

**Question 4 :**

Simplify (-7x²) (x⁴)

**Solution :**

= (-7x²) (x⁴)

= -7 x⁽²⁺⁴⁾

= -7 x⁶

**Question 5 :**

Simplify (10 x y³ z²) (-2 x y⁵z)

**Solution :**

= (10 x y³ z²) (-2 x y⁵z)

= -20 x^(1+1) y^(3+5) z^(2+1)

= -20 x²y⁸z³

**Question 6 :**

Simplify (-5 xyz) (4 y⁵z) y³

**Solution :**

= (-5 xyz) (4 y⁵z) y³

= -20 x y⁵y³z z

= -20 x y^(5+3) z^(1+1)

= - 20 x y⁸z²

**Question 7 :**

Simplify (7 a b² c³) (¾ a b c⁴)

**Solution :**

= (7 a b² c³) (¾ a b c⁴)

= (21/4) a^(1+1)b^(2+1)c^(3+4)

= (21/4) a²b³c⁷

**Question 8 :**

Simplify (-4 a³) (-5 a⁴)

**Solution :**

= (-4 a³) (-5 a⁴)

= 20 a^(3+4)

= 20 a⁷

**Question 9 :**

Simplify (2 a³) (¼) a⁴

**Solution :**

= (2 a³) (¼) a⁴

= (2/4)a^(3+4)

= (1/2) a⁷

**Question 10 :**

Simplify (10 p³) (7/25) p⁷

**Solution :**

= (10 p³) (7/25) p⁷

= 10(7/25)p^(3+7)

= (1/2) a¹⁰

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