QUOTIENT RULE OF EXPONENTS

Quotient Rule of Exponents :

When dividing exponential expression that have the same base, subtract the exponents.

aman = am-n

Example 1 :

x3x

Solution :

= x3x aman=am-n= x3-1= x2

Example 2 :

18c3-3c2

Solution :

= 18c3-3c2= -6c3-2= -6c

Example 3 :

9a3b5-3ab2

Solution :

9a3b5-3ab2= -3a3-1b5-2= -3a2b3

Example 4 :

-48c2d4-8cd

Solution :

= -48c2d4-8cd=6c2-1d4-1=6cd3

Example 5 :

22y6z82yz-7

Solution :

22y6z82yz-7=11y6-1z8+7=11y5z

Example 6 :

2x3-8x4

Solution :

= 2x3-8x41 4x3-41 4x-1

Example 7 :

xy7x3y4

Solution :

xy7x3y4= x1-3 y7-4= x-2 y3

Example 8 :

6x⋅ 3x⋅ x0

Solution :

Multiply the coefficients,

= 6x⋅ 3x⋅ x0

= (6 × 3)(x⋅ x⋅ x0)

By a⋅ an = am+n,

= 18(x5+5 ⋅ x0)

= 18(x10⋅ x0)

= 18x10

Example 9 :

(3st12)3

Solution :

(3st12)3

= 33s3(t12)3

= 27s3(t12)3

By (am)n = amn,

= 27s3t(12×3)

 27s3t36

Example 10 :

3m2n7m5

Solution :

3m2n7m5amn= amn(3)5m10n35m5amanam-n243m10-5n35= 243m5n35

Example 11 :

20x-427y28x-315y-5

Solution :

=20x-427y2 ÷ 8x-315y-5Multiply by the reciprocal of 8x-315y-5= 20x-427y2 × 15y-58x-3= 5x-49y2 × 5y-52x-3= 2518 x-4 . y-2 . y-5 . x3Combining like terms,= 2518 x-4 . x3 . y-5 . y-2= 2518 x-4+3 . y-5-2= 2518 x-1 . y-7= 2518 x-1y-7

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