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  1. Maths
  2. Year 8
  3. Algebra: Expressions
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Powers of Algebraic Powers (2)

In this worksheet, students must simplify powers of algebraic powers.

'Powers of Algebraic Powers (2)' worksheet

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Simplify Algebraic Expressions to Maintain Equivalence

Difficulty level:  

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Worksheet Overview

QUESTION 1 of 10

This worksheet is about simplifying powers of algebraic powers.

 

Example

Simplify:

(a3b2)4

 

 

Answer

Remember what to the power of 4 means and multiply the terms 4 times.

We get:    

a3b2 × a3b2 × a3b2 × a3b2

 

Add the indices of matching identical letters

(for the letter a: 3 + 3 + 3 + 3 = 12 and for the letter b: 2 + 2 + 2 + 2 = 8).

 

Answer is a12b8.

Simplify:

(a3b)2

a32b2

a5b

a6b2

Simplify:

(a2b2)2

a22b22

a4b4

a4b2

Simplify:

(a3b2)2

a32b22

a6b4

a6b2

Simplify:

(ab2)2

ab4

a2b4

ab2

Simplify:

(cb2)3

c3b6

c2b4

cb6

Simplify:

(c3d2)3

c3d6

c6d5

c9d6

Simplify:

(f3d2)4

f7d6

f6d5

f12d8

Simplify:

(f3g)4

f7g4

f12g4

f12g

Simplify:

(p3q)6

p18q6

p9q6

p18q

Simplify:

(p3q4)7

p10q11

p21q11

p21q28

  • ANSWERS
  • Question 1

Simplify:

(a3b)2

CORRECT ANSWER
a6b2
EDDIE SAYS
a3b × a3b
Then add the indices.
a3 × a3 × b × b
  • ANSWERS
  • Question 2

Simplify:

(a2b2)2

CORRECT ANSWER
a4b4
EDDIE SAYS
a2b2 × a2b2
a2 × a2 × b2 × b2
  • ANSWERS
  • Question 3

Simplify:

(a3b2)2

CORRECT ANSWER
a6b4
EDDIE SAYS
a3b2 × a3b2
a3 × a3 × b2 × b2
  • ANSWERS
  • Question 4

Simplify:

(ab2)2

CORRECT ANSWER
a2b4
EDDIE SAYS
ab2 × ab2
a × a × b2 × b2
  • ANSWERS
  • Question 5

Simplify:

(cb2)3

CORRECT ANSWER
c3b6
EDDIE SAYS
cb2 × cb2 × cb2
c × c × c × b2 × b2 × b2
  • ANSWERS
  • Question 6

Simplify:

(c3d2)3

CORRECT ANSWER
c9d6
EDDIE SAYS
c3d2 × c3d2 × c3d2
c3 × c3 × c3 × d2 × d2 × d2
  • ANSWERS
  • Question 7

Simplify:

(f3d2)4

CORRECT ANSWER
f12d8
EDDIE SAYS
f3d2 × f3d2 × f3d2 × f3d2
f3 × f3 × f3 × f3 × d2 × d2 × d2 × d2
  • ANSWERS
  • Question 8

Simplify:

(f3g)4

CORRECT ANSWER
f12g4
EDDIE SAYS
f3g × f3g × f3g × f3g
f3 × f3 × f3 × f3 × g × g × g × g
  • ANSWERS
  • Question 9

Simplify:

(p3q)6

CORRECT ANSWER
p18q6
EDDIE SAYS
p3q × p3q × p3q × p3q × p3q × p3q
p3 × p3 × p3 × p3 × p3 × p3 × q × q × q × q × q × q
  • ANSWERS
  • Question 10

Simplify:

(p3q4)7

CORRECT ANSWER
p21q28
EDDIE SAYS
p3q4 × p3q4 × p3q4 × p3q4 × p3q4 × p3q4 × p3q4
p3 × p3 × p3 × p3 × p3 × p3 × p3 × q4 × q4 × q4 × q4 × q4 × q4 × q4
---- OR ----

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