Rules of Exponents Assessment – 10/23/15
Topics on Exponent Assessment
Product Rules
 When multiplying the same base, add exponents.
𝑥 4 ∙ 𝑥 5 = 𝑥 4+5 = 𝑥 9

When there is a power to a power, multiply the exponents.
(𝑥 6 )5 = 𝑥 6⦁5 = 𝑥 30

When there is a power of a product, apply the exponent to each factor.
(𝑥𝑦)3 = 𝑥 3 𝑦 3
Quotient Rules
 When dividing the same base, subtract exponents.
𝑥6
𝑥4

= 𝑥 6−4 = 𝑥 2 , 𝑥 ≠ 0
When there is a quotient to a power, distribute the exponent to everything in the numerator and denominator.
𝑥 5
𝑥5
( ) = 5 ,𝑦 ≠ 0
𝑦
𝑦
Zero and Negative Exponents
 Any number to the zero power is equal to one.
𝑥 0 = 1, 𝑥 ≠ 0 Notice in this example 𝑥 ≠ 0. This because 00 is undefined.

Any number to a negative power is the reciprocal of the number to a positive exponent.
1. 𝑥 −2 =
1
,
𝑥2
𝑥 ≠0
𝑜𝑟
2.
1
𝑥 −2
=
𝑥2
1
= 𝑥2
Notice in example 1 that 𝑥 ≠ 0. This is because 0 would end up in the denominator and when 0 is in the
denominator it is undefined.
Helpful hints
Remember if you get stuck – E
X P A N D!
Remember the rules of exponents apply only to exponents not the bases.

When multiplying the same base, add the exponents. Do not add or multiply the bases.
Example:
Wrong 45 ⦁49 ≠ 814
Wrong 45 ⦁49 ≠ 1614
Right 45 ⦁49 = 414
More Helpful hints

When dividing the same base, subtract the exponents. Do not subtract the bases.
Example:

85
83
≠ 12
85
83
= 82
Wrong
16𝑥 7
12𝑥 2
≠ 4𝑥 5
Right
16𝑥 7
12𝑥 2
=
4𝑥 5
3
because
16
12
simplifies to
4
3
Negative exponents do not make a positive base negative or a negative base positive.
Example:
Wrong 5−3 ≠ −53
Right 5−3 =

Right
Do not apply rules of exponents to any base. Do not subtract coefficients of fractions, simplify them.
Example:

Wrong
1
53
𝑜𝑟
Wrong
1
125
Right
1
(−8)−6
1
(−8)−6
≠
=
1
86
86
1
= 86
When simplifying a more complex expression. Do it step by step applying one rule a time.
2
2
2
33𝑎6 𝑏−2 𝑐 5
3𝑎6 𝑎3
3𝑎9
32 𝑎18
9𝑎18
(
) = ( 6 2 2 ) = ( 8 2 ) = 16 4 = 16 4
11𝑎−3 𝑏 6 𝑐 7
𝑏 𝑏 𝑐
𝑏 𝑐
𝑏 𝑐
𝑏 𝑐
Some helpful links:
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/World-of-exponents/v/understanding-exponents
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/World-of-exponents/v/understanding-exponents-2
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/v/exponent-rules-part-1
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/v/exponent-rules-part-2
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/e/exponent_rules
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/e/properties-of-integerexponents
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/World-of-exponents/v/powers-of-zero
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/World-of-exponents/v/raising-a-number-to-the0th-and-1st-power
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/negative-exponents-tutorial/v/negativeexponents
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/negative-exponents-tutorial/e/exponents_2
http://www.mesacc.edu/~scotz47781/mat120/notes/exponents/review/review.html