University:
Bradley University
Course:
MTH 112 | Precalculus
Academic year:

2024
Views:

86

Pages:

2
Author:

Remington Spence

Exponent Rules Review Worksheet NOTE: Anything to the zero power equals 1! Product Rule: When multiplying monomials that have the same base, add the exponents. x m  x n  x m n Example 1: x  x3  x4  x134  x8 Example 2:  2x y  3x y   2   3  x 2 3 4 2  x3  y  y 4  6 x5 y 5 Power Rule: When raising monomials to powers, multiply the exponents. x  m n  x m n Example 3: (x2y3)4 = x2  4 y3  4 = x8y12 Example 4: (2x3yz2)3 = 23 x3  3 y3 z2  3 = 8x9y3z6 Quotient Rule: When dividing monomials that have the same base, subtract the exponents. xm  x mn n x x3 36m3n5 36 m3 n5 56 Example 5: 2  x3( 2)  x5 Example 6: 2  562  54 Example 7:    4  4m2 n 4 x 9mn 9 m n 5 Simplify each of the following. Copy the problem. Work on your own paper. 1) a  a2  a3 2) 6) (2x2y3)2 7) (5x2y4)3 11) x3 x 12) (2a2b)(4ab2) 18c3 3c 2 3) (6x2)(-3x5) 8) (6x4y6)3 13) 9a3b5 3ab2 16) x2  x7 17)  x 2  21) 8x0 22) 34 23)  3 2 x3 26) 8 x 4 xy 7 27) 3 4 x y 28) 6x  3x  x 7 18)  2x 4  5 4) b3  b4  b7  b 5) (3x3)(3x4)(-3x2) 9) (4x3y3)3 10) (7xy)2 14) 5 48c 2 d 4 8cd 19) 2x3  7 x3 24) 6 x 0 y 8   2 y 2  4 5 15) 0 29)  3st 12  3 22 y 6 z 8 2 yz 7 20) 70 4 25)  x  2 y  x  2 y   3m 2 n 7  30)    m  5 Exponent Rules Review Worksheet NOTE: Anything to the zero power equals 1! Product Rule: When multiplying monomials that have the same base, add the exponents. x m  x n  x m n Example 1: x  x3  x4  x134  x8 Example 2:  2x y  3x y   2   3  x 2 3 4 2  x3  y  y 4  6 x5 y 5 Power Rule: When raising monomials to powers, multiply the exponents. x  m n  x m n Example 3: (x2y3)4 = x2  4 y3  4 = x8y12 Example 4: (2x3yz2)3 = 23 x3  3 y3 z2  3 = 8x9y3z6 Quotient Rule: When dividing monomials that have the same base, subtract the exponents. xm  x mn n x x3 36m3n5 36 m3 n5 56 Example 5: 2  x3( 2)  x5 Example 6: 2  562  54 Example 7:    4  4m2 n 4 x 9mn 9 m n 5 Simplify each of the following. Copy the problem. Work on your own paper. 1) a  a2  a3 2) 6) (2x2y3)2 7) (5x2y4)3 11) x3 x 12) (2a2b)(4ab2) 18c3 3c 2 3) (6x2)(-3x5) 8) (6x4y6)3 13) 9a3b5 3ab2 16) x2  x7 17)  x 2  21) 8x0 22) 34 23)  3 2 x3 26) 8 x 4 xy 7 27) 3 4 x y 28) 6x  3x  x 7 18)  2x 4  5 4) b3  b4  b7  b 5) (3x3)(3x4)(-3x2) 9) (4x3y3)3 10) (7xy)2 14) 5 48c 2 d 4 8cd 19) 2x3  7 x3 24) 6 x 0 y 8   2 y 2  4 5 15) 0 29)  3st 12  3 22 y 6 z 8 2 yz 7 20) 70 4 25)  x  2 y  x  2 y   3m 2 n 7  30)    m  5

Exponent Rules Worksheet

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