# APPLY EXPONENT PROPERTIES INVOLVING PRODUCTS WORKSHEETS

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.

## Apply exponent properties involving products worksheets - Questions

(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 x⁶/13x⁷)

(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) a

(10) Simplify  (10 p³) (7/25) p

## Apply exponent properties involving products worksheets - Solution

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 ²⁾ then find the value of n.

Solution :

Question 3 :

Simplify  (52 x⁶/13x⁷)

Solution :

=  (52 x⁶/13x⁷)

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 xx/13)

=  4 x

=  4 x¹³

Question 4 :

Simplify  (-7x²) (x⁴)

Solution :

=  (-7x²) (x⁴)

=  -7 x²

=  -7 x

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 yy³z

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

= - 20 x yz²

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) a²b³c

Question 8 :

Simplify  (-4 a³) (-5 a⁴)

Solution :

=    (-4 a³) (-5 a⁴)

20 a^(3+4)

= 20 a

Question 9 :

Simplify  (2 a³) (¼) a

Solution :

=    (2 a³) (¼) a

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

= (1/2) a

Question 10 :

Simplify  (10 p³) (7/25) p

Solution :

=   (10 p³) (7/25) p

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

= (1/2) a¹

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