Powers and Roots - Opinions Nobody Asked For - Free Printable

Let's solve each expression step by step and fill in the blanks.

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Left Column:

1. $ 3^3 + 3 = ? $
$ 3^3 = 27 $, so $ 27 + 3 = \boxed{30} $

2. $ 2^3 + 2 = ? $
$ 2^3 = 8 $, so $ 8 + 2 = \boxed{10} $

3. $ 1^3 + 6^3 + 10 = ? $
$ 1^3 = 1 $, $ 6^3 = 216 $, so $ 1 + 216 + 10 = \boxed{227} $

4. $ 2^3 + 3^3 = ? $
$ 2^3 = 8 $, $ 3^3 = 27 $, so $ 8 + 27 = \boxed{35} $

5. $ 5^3 - 2^3 = ? $
$ 5^3 = 125 $, $ 2^3 = 8 $, so $ 125 - 8 = \boxed{117} $

6. $ 7^2 - 2^3 = ? $
$ 7^2 = 49 $, $ 2^3 = 8 $, so $ 49 - 8 = \boxed{41} $

7. $ 4^3 - 4^2 = ? $
$ 4^3 = 64 $, $ 4^2 = 16 $, so $ 64 - 16 = \boxed{48} $

8. $ 8^2 - 4^3 = ? $
$ 8^2 = 64 $, $ 4^3 = 64 $, so $ 64 - 64 = \boxed{0} $

9. $ 10^2 + 5^3 = ? $
$ 10^2 = 100 $, $ 5^3 = 125 $, so $ 100 + 125 = \boxed{225} $

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Right Column:

1. $ 12^2 + 11^2 = ? $
$ 12^2 = 144 $, $ 11^2 = 121 $, so $ 144 + 121 = \boxed{265} $

2. $ 3^3 \times 3^2 = ? $
$ 3^3 = 27 $, $ 3^2 = 9 $, so $ 27 \times 9 = \boxed{243} $
*Alternatively:* $ 3^{3+2} = 3^5 = 243 $

3. $ 7^2 \times 4^3 = ? $
$ 7^2 = 49 $, $ 4^3 = 64 $, so $ 49 \times 64 $
Let's compute:
$ 50 \times 64 = 3200 $, subtract $ 1 \times 64 = 64 $ → $ 3200 - 64 = \boxed{3136} $

4. $ 10^2 \times 10^2 \times 10^2 = ? $
$ 10^2 = 100 $, so $ 100 \times 100 \times 100 = 1,000,000 $
Or: $ 10^{2+2+2} = 10^6 = \boxed{1,000,000} $

5. $ 6^3 \div 3 = ? $
$ 6^3 = 216 $, so $ 216 \div 3 = \boxed{72} $

6. $ 12^2 \div 3 = ? $
$ 12^2 = 144 $, so $ 144 \div 3 = \boxed{48} $

7. $ 6^3 \div 10^2 = ? $
$ 6^3 = 216 $, $ 10^2 = 100 $, so $ 216 \div 100 = \boxed{2.16} $

8. $ \dfrac{7^2 \times 3^3}{10^2} = ? $
$ 7^2 = 49 $, $ 3^3 = 27 $, $ 10^2 = 100 $
Numerator: $ 49 \times 27 $
$ 50 \times 27 = 1350 $, minus $ 1 \times 27 = 27 $ → $ 1350 - 27 = 1323 $
So $ \dfrac{1323}{100} = \boxed{13.23} $

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✔ Final Answers:

#### Left Column:
1. $ 3^3 + 3 = \boxed{30} $
2. $ 2^3 + 2 = \boxed{10} $
3. $ 1^3 + 6^3 + 10 = \boxed{227} $
4. $ 2^3 + 3^3 = \boxed{35} $
5. $ 5^3 - 2^3 = \boxed{117} $
6. $ 7^2 - 2^3 = \boxed{41} $
7. $ 4^3 - 4^2 = \boxed{48} $
8. $ 8^2 - 4^3 = \boxed{0} $
9. $ 10^2 + 5^3 = \boxed{225} $

#### Right Column:
1. $ 12^2 + 11^2 = \boxed{265} $
2. $ 3^3 \times 3^2 = \boxed{243} $
3. $ 7^2 \times 4^3 = \boxed{3136} $
4. $ 10^2 \times 10^2 \times 10^2 = \boxed{1,000,000} $
5. $ 6^3 \div 3 = \boxed{72} $
6. $ 12^2 \div 3 = \boxed{48} $
7. $ 6^3 \div 10^2 = \boxed{2.16} $
8. $ \dfrac{7^2 \times 3^3}{10^2} = \boxed{13.23} $

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