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(Answer) MATH114N – Week 2 Assignment: Quotient Properties of Exponents and Dividing Monomials

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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