Squares and Cubes of Monomials
A. Fill in the blank boxes.
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number
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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square of number
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25
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cube of number
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216
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skip
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skip
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WATCH OUT: Do you know that 32 = 9 but (x3)2 is x6 ?
32 is 3 times 3 = 9 (x3)2 is (x3)(x3) =x6
So what is (x4)3 ? Write the (x4) three times for multiplying (x4)(x4)(x4). What does this equal?
HINT: How many x will we have multiplied?
For squaring write the whole expression twice and then use multiplying rules.
(x3)2 is (x3)(x3) which is (xxx)(xxx) = x6
For cubing write the whole expression thrice and then use multiplying rules.
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number/variable
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x
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y
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2m
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x2
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xy2
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5m2
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6x3
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b2y3
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3m3
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4x4
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x2y4
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square of number/variable
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36x6
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cube of number/variable
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x6
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b6y9
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B. Fill in the blank boxes. There may be repeats of a whole column.
I would suggest first finding the top row in each table.
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number
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square of number
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16
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64
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49
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81
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25
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cube of number
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1
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8
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27
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125
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64
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C. Fill in the blank boxes.
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number/variable
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x
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3x2
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3v2
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square of number/variable
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y2
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81m2
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64b4
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9r4
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81b6
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cube of number/variable
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y3
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27v6
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64z3
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8x3
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fourth power of number/variable
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x4
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D Study the first list of squares. Do you know what number I squared to get these?
Finish the other 3 that I have started so you know these well.
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1
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49
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169
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49
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1
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169
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1
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4
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64
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196
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4
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196
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9
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81
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225
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9
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16
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100
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400
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25
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121
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900
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36
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144
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2500
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2500
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36
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Susan O. Johnsey 2003 -2011, 2012 sjohnsey@bellsouth.net
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