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Worksheets

Laws of Exponents Review

Total questions: 14

Worksheet time: 1hrs 10mins

Name
Class
Date
1.

Simplify the expression.  −x4y−4(yx−3z−4⋅−2x3y−1)−2-\frac{x^4y^{-4}}{\left(yx^{-3}z^{-4}\cdot-2x^3y^{-1}\right)^{-2}}  

a)

 yz6x12\frac{yz^6}{x^{12}}  

b)

 −4x4y4z8-\frac{4x^4}{y^4z^8}  

c)

 −x2z62y-\frac{x^2z^6}{2y}  

d)

 y32x6z8\frac{y^3}{2x^6z^8}  

2.

Simplify the expression.  −y−4z2⋅y0z2(2z−4)3-\frac{y^{-4}z^2\cdot y^0z^2}{\left(2z^{-4}\right)^3}  

a)

 −z168y4-\frac{z^{16}}{8y^4}  

b)

 −y24x18-y^{24}x^{18}  

c)

 y3x\frac{y^3}{x}  

d)

 x4z64y7\frac{x^4z^6}{4y^7}  

3.

 (2y02x4y4⋅x)2\left(\frac{2y^0}{2x^4y^4\cdot x}\right)^2  

a)

 1x10y8\frac{1}{x^{10}y^8}  

b)

 4y6x\frac{4y^6}{x}  

c)

 x102y\frac{x^{10}}{2y}  

d)

 x16y3\frac{x^{16}}{y^3}  

4.

 (2u2⋅2u2u2v0)2\left(\frac{2u^2\cdot2u}{2u^2v^0}\right)^2  

a)

 64v60u42\frac{64v^{60}}{u^{42}}  

b)

 8v5u5\frac{8v^5}{u^5}  

c)

 4u24u^2  

d)

 1u24v32\frac{1}{u^{24}v^{32}}  

5.

Simplify the expression (2a0)2⋅2ab−1ab−4\frac{\left(2a^0\right)^2\cdot2ab^{-1}}{ab^{-4}}  

a)

 b15a38\frac{b^{15}a^3}{8}  

b)

 b1616a8\frac{b^{16}}{16a^8}  

c)

 8b38b^3  

d)

 ba72\frac{ba^7}{2}  

6.

Simplify the expression. 2y(xyx0)−1\frac{2y}{\left(xyx^0\right)^{-1}}  

a)

 x10y6\frac{x^{10}}{y^6}  

b)

 x16y4\frac{x^{16}}{y^4}  

c)

 2xy22xy^2  

d)

 x64y8\frac{x^6}{4y^8}  

7.

Simplify the expression x22x−1y3⋅2y−4\frac{x^2}{2x^{-1}y^3\cdot2y^{-4}}  

a)

 x3y4\frac{x^3y}{4}  

b)

 14y12x\frac{1}{4y^{12}x}  

c)

 x32\frac{x^3}{2}  

d)

 2y4x2\frac{2y^4}{x^2}  

8.

 (m3n4)−3nm0⋅2m2\frac{\left(m^3n^4\right)^{-3}}{nm^0\cdot2m^2}  

a)

 n3mn^3m  

b)

 12m11n13\frac{1}{2m^{11}n^{13}}  

c)

 1n12\frac{1}{n^{12}}  

d)

 2m9n6\frac{2m^9}{n^6}  

9.

 2vu−4⋅2u3v3(u2v3)3\frac{2vu^{-4}\cdot2u^3v^3}{\left(u^2v^3\right)^3}  

a)

 1v6u2\frac{1}{v^6u^2}  

b)

 2u14v13\frac{2}{u^{14}v^{13}}  

c)

 4u7v5\frac{4}{u^7v^5}  

d)

 1v14u13\frac{1}{v^{14}u^{13}}  

10.

 (2x0((2xy−3)−1⋅2y)4)2\left(\frac{2x^0}{\left(\left(2xy^{-3}\right)^{-1}\cdot2y\right)^4}\right)^2  

a)

 4x6\frac{4}{x^6}  

b)

 x9y3\frac{x^9}{y^3}  

c)

 2x5y22x^5y^2  

d)

 4x8y32\frac{4x^8}{y^{32}}  

11.

 9x6y2⋅5x2y39x^6y^2\cdot5x^2y^3  

a)

 14x8y514x^8y^5  

b)

 14x12y614x^{12}y^6  

c)

 45x8y545x^8y^5  

d)

 45x12y645x^{12}y^6  

e)

 45x8y645x^8y^6  

12.

 7a4b⋅(−3a5b6)27a^4b\cdot\left(-3a^5b^6\right)^2  

a)

 63a40b1263a^{40}b^{12}  

b)

 −42a40b12-42a^{40}b^{12}  

c)

 −63a14b13-63a^{14}b^{13}  

d)

 63a14b1363a^{14}b^{13}  

13.

 18w15v106w3v2\frac{18w^{15}v^{10}}{6w^3v^2}  

a)

 12w12v812w^{12}v^8  

b)

 3w12v83w^{12}v^8  

c)

 3w5v53w^5v^5  

d)

 12w5v512w^5v^5  

14.

 (8m6n4)34m3n2\frac{\left(8m^6n^4\right)^3}{4m^3n^2}  

a)

 128m15n10128m^{15}n^{10}  

b)

 128m6n6128m^6n^6  

c)

 6m15n106m^{15}n^{10}  

d)

 6m6n66m^6n^6