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Worksheets

Simplifying and Evaluating Powers

Total questions: 26

Worksheet time: 28mins

Name
Class
Date
1.

Simplify

 (x2y)3\left(x^{-2}\cdot y\right)^{-3}  

a)

 x6y3\frac{x^6}{y^3}  

b)

 1x5y3\frac{1}{x^5y^3}  

c)

 x6y3-x^6y^3  

d)

 x5y3\frac{x^5}{y^3}  

2.

Simplify
 12x53x7\frac{12x^5}{3x^7}  

a)

 4x24x^2  

b)

 14x2\frac{1}{4x^2}  

c)

 9x2\frac{9}{x^2}  

d)

 4x2\frac{4}{x^2}  

3.

Simplify: 2x2-2x^{-2}  

a)

 12x2\frac{1}{2x^2}  

b)

 2x2\frac{-2}{x^2}  

c)

 4x2\frac{4}{x^2}  

d)

 14x2\frac{1}{4x^2}  

4.

Simplify: (8x25)2\left(\frac{8x}{25}\right)^{-2}  

a)

 825x2\frac{8}{25x^2}  

b)

 625x264\frac{-625x^2}{64}  

c)

 62564x2\frac{625}{64x^2}  

d)

 64625x2\frac{64}{625x^2}  

5.

Simplify: (a9b2c8)6\left(a^9b^{-2}c^8\right)^6  

a)

 a54c48b12\frac{a^{54}c^{48}}{b^{12}}  

b)

 a54b12c48a^{54}b^{12}c^{48}  

c)

 a15b4c14a^{15}b^4c^{14}  

d)

 a15b8c14a^{15}b^8c^{14}  

6.

Simplify: (xy4)5\left(\frac{x}{y^4}\right)^5  

a)

 x5y9\frac{x^5}{y^9}  

b)

 x5y20\frac{x^5}{y^{20}}  

c)

 1xy4\frac{1}{xy^4}  

d)

 xy4xy^4  

7.

Simplify: x4y6x2y5z\frac{x^{-4}y^{-6}}{x^2y^5z}  

a)

 1x6y11z\frac{1}{x^6y^{11}z}  

b)

 1x2yz\frac{1}{x^2yz}  

c)

 zx6y11\frac{z}{x^6y^{11}}  

d)

 x6y11zx^6y^{11}z  

8.

Simplify: (x2y2)2x4y19\left(x^2y^2\right)^{-2}\cdot x^4y^{19}  

a)

 x4y19x^4y^{19}  

b)

 xy15xy^{15}  

c)

 y15y^{15}  

d)

 1x16y76\frac{1}{x^{16}y^{76}}  

9.

Simplify: (v2)4(10v)3\left(\frac{v}{2}\right)^4\left(\frac{10}{v}\right)^3  

a)

 5v75v^7  

b)

 125v72\frac{125v^7}{2}  

c)

 125v2\frac{125v}{2}  

d)

 5v5v  

10.

Evaluate

 3336\frac{3^{-3}}{3^{-6}}  

a)

 127\frac{1}{27}  

b)

 2727  

c)

 127-\frac{1}{27}  

d)

 27-27  

11.
Simplify: 
(-4r3s5)0 (3b4c2d)
a)
1
b)
-12b4c2d
c)
3b4c2d
d)
0
12.
Simplify: 
(-2)³⋅(-2)⁶
a)
(-2)⁹
b)
(-2)¹⁸
c)
(-2)⁻³
d)
(-2)
13.

Identify the equivalent form.

a)

44/3

b)

43/4

c)

24/3

d)

23/4

14.

Identify the equivalent form.

a)

23/5

b)

-23/5

c)

25/3

d)

85

15.

Identify the equivalent form.

a)

216

b)

61/2

c)

62

d)

63/2

16.

Identify the equivalent form.

a)

5x5/4

b)

5x-5/4

c)

(5x)-5/4

d)

(5x)-4/5

17.

Check all that is true

Simplify the expression:

271/3

a)

3

b)

9

c)

∛27

d)

33

18.
Write as a radical expression
y¹⁄ ³
a)
∛y
b)
c)
√y
d)
1∕ 3y
19.

 8138^{\frac{1}{3}}   check at that applies

a)

24

b)

2

c)

cubed root of 8

d)

512

20.

Check all that applies

a)

8

b)

4

c)

1024

d)

2561/4

21.

an exponent 1/2 means

a)

square root

b)

cube root

c)

fourth root

d)

fifth root

22.

Identify the equivalent form.

 21z1221z^{\frac{1}{2}}  

a)

 21221^2   z2z^2  

b)

21 z2z^2  

c)

 21z\sqrt{21z}  

d)

21 z\sqrt{z}  

23.
Write as a radical expression
y²⁄ ³
a)
2y³
b)
√y³
c)
∛y²
d)
3y²
24.
Simplify
a)
2∛-2
b)
1 / (2∛-2)
c)
-1/2
d)
Not possible
25.
Simplify 
a)
2x2yz2 ⁵√(xy3)
b)
2x2yz4 ⁵√(xy3)
c)
2xyz ⁵√(xy3z)
d)
2x2yz4 ⁵√(xy3z)
26.

Identify the equivalent form.

a)

216

b)

61/2

c)

62

d)

63/2