QUESTIONS:
Question 1
Simplify: (4/3q)4. You may assume that any variables are nonzero.
Question 2
Simplify: (4/2n)3. You may assume that any variables are nonzero.
Question 3
Simplify: (−4m3)2 (5m4)3 /(−10m6)3
Question 4
Simplify: 52/523. Write the answer using a positive exponent.
Question 5
Find the quotient: (6u11v6) (11u5v) / −44u11v12.
Question 6
Find the quotient: −2c2d10 / (−12c3d7)(18c9d8).
Question 7
Simplify: (−10n2)3 (4n5)2 / (2n8)2
Question 8
Simplify: 94 / 924
Report your answer as a fraction.
Question 9
Simplify: 12n0 – 18m0
Question 10
Simplify: (−93c7d15)0
Question 11
Simplify: (c/4c)2. You may assume that any variables are nonzero.
Question 12
Simplify: (m/w)6 You may assume that any variables are nonzero.
Question 13
Find the quotient: 22m11n8 / -44m12n8
Question 14
Find the quotient: 64x10y / −14x12y4
Question 15
Simplify: (−2p2)4(3p4)2(−6p3)2.
Question 16
Simplify: (k2k8/k3)2
SOLUTIONS:
Question 1
Simplify: (4/3q)4. You may assume that any variables are nonzero.
Answer
256 / 81q4
Question 2
Simplify: (4/2n)3. You may assume that any variables are nonzero.
Answer
8/n3
Question 3
Simplify: (−4m3)2 (5m4)3 /(−10m6)3
Answer
−2
To simplify (−4m3)2 (5m4)3 / (−10m6)3, first use the Product to a Power Property, (ab)m = ambm, and the Power Property, (am)n = am.n, to simplify the numerator and denominator as follows.
(−4m3)2 (5m4)3 / (−10m6)3 = (−4)2(m3)2(5)3(m4)3 / (−10)3(m6)3
= 16m6 ⋅ 125m12 / −1,000m18
= −2m18/m18
Using the Quotient Property, am / an = am-n, the expression becomes
−2m18 / m18 = −2m18-18
= −2m0
= −2
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