Recall that to simplify an expression means to rewrite it by combing terms or exponents; in other words, to write the expression more simply with fewer terms. The rules for exponents may be combined to simplify expressions.
Example 9: Simplifying Exponential Expressions
Simplify each expression and write the answer with positive exponents only.
(6m2n−1)3
175⋅17−4⋅17−3
(v−1u−1v)2
(−2a3b−1)(5a−2b2)
(x22)4(x22)−4
(6w−2)2(3w2)5
Solution
(6m2n−1)3====(6)3(m2)3(n−1)363m2⋅3n−1⋅3216m6n−3n3216m6The power of a product ruleThe power ruleSimplify.The negative exponent rule
175⋅17−4⋅17−3===175−4−317−21721 or 2891The product ruleSimplify.The negative exponent rule
(v−1u−1v)2=====(v−1)2(u−1v)2v−2u−2v2u−2v2−(−2)u−2v4u2v4The power of a quotient ruleThe power of a product ruleThe quotient ruleSimplify.The negative exponent rule
(−2a3b−1)(5a−2b2)===−2⋅5⋅a3⋅a−2⋅b−1⋅b2−10⋅a3−2⋅b−1+2−10abCommutative and associative laws of multiplicationThe product ruleSimplify.
(x22)4(x22)−4===(x22)4−4(x22)01The product ruleSimplify.The zero exponent rule
(6w−2)2(3w2)5=====(6)2⋅(w−2)2(3)5⋅(w2)562w−2⋅235w2⋅536w−4243w10427w10−(−4)427w14The power of a product ruleThe power ruleSimplify.The quotient rule and reduce fractionSimplify.
Try It 9
Simplify each expression and write the answer with positive exponents only.
a. (2uv−2)−3
b. x8⋅x−12⋅x
c. (f−1e2f−3)2
d. (9r−5s3)(3r6s−4)
e. (94tw−2)−3(94tw−2)3
f. (7h−1k2)2(2h2k)4
Solution
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College Algebra.Provided by: OpenStaxAuthored by: OpenStax College Algebra.Located at: https://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1/Preface.License: CC BY: Attribution.