Digital Math Activity Bundle 7th Grade - Free Printable

Let's solve each of these exponent problems step by step. We'll evaluate each expression using the rules of exponents, especially focusing on negative bases, even/odd powers, and negative exponents.

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🔢 Rules to Remember:

1. Even power of a negative number → positive
$(-a)^{even} = positive$

2. Odd power of a negative number → negative
$(-a)^{odd} = negative$

3. Negative exponent:
$a^{-n} = \frac{1}{a^n}$

4. Zero exponent: $a^0 = 1$ (not needed here)

5. Positive exponents: Multiply the base by itself that many times.

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Now, let’s go through each problem:

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1) $(-8)^2 = ?$

- Even power → positive
- $(-8)^2 = (-8) \times (-8) = 64$

✔ Answer: 64

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2) $(4)^3 = ?$

- $4 \times 4 \times 4 = 64$

✔ Answer: 64

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3) $(10)^2 = ?$

- $10 \times 10 = 100$

✔ Answer: 100

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4) $(-6)^4 = ?$

- Even power → positive
- $(-6)^4 = (-6) \times (-6) \times (-6) \times (-6)$
- First: $(-6)^2 = 36$, then $36^2 = 1296$

✔ Answer: 1296

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5) $(-9)^3 = ?$

- Odd power → negative
- $(-9)^3 = (-9) \times (-9) \times (-9)$
- $= 81 \times (-9) = -729$

✔ Answer: -729

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6) $(-10)^2 = ?$

- Even power → positive
- $(-10)^2 = 100$

✔ Answer: 100

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7) $(12)^2 = ?$

- $12 \times 12 = 144$

✔ Answer: 144

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8) $(6)^4 = ?$

- $6^2 = 36$, so $6^4 = 36^2 = 1296$

✔ Answer: 1296

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9) $(3)^4 = ?$

- $3^2 = 9$, $3^4 = 9^2 = 81$

✔ Answer: 81

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10) $(-2)^{-7} = ?$

- Negative exponent → reciprocal
- $(-2)^{-7} = \frac{1}{(-2)^7}$
- $(-2)^7 = -128$ (since odd power)
- So: $\frac{1}{-128} = -\frac{1}{128}$

✔ Answer: $-\frac{1}{128}$

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11) $(-2)^{-8} = ?$

- $(-2)^{-8} = \frac{1}{(-2)^8}$
- $(-2)^8 = 256$ (even power → positive)
- So: $\frac{1}{256}$

✔ Answer: $\frac{1}{256}$

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12) $(-3)^{-4} = ?$

- $(-3)^{-4} = \frac{1}{(-3)^4}$
- $(-3)^4 = 81$
- So: $\frac{1}{81}$

✔ Answer: $\frac{1}{81}$

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13) $(5)^2 = ?$

- $5 \times 5 = 25$

✔ Answer: 25

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14) $(2)^3 = ?$

- $2 \times 2 \times 2 = 8$

✔ Answer: 8

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15) $(-12)^{-2} = ?$

- $(-12)^{-2} = \frac{1}{(-12)^2}$
- $(-12)^2 = 144$
- So: $\frac{1}{144}$

✔ Answer: $\frac{1}{144}$

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16) $(-3)^{-5} = ?$

- $(-3)^{-5} = \frac{1}{(-3)^5}$
- $(-3)^5 = -243$ (odd power)
- So: $\frac{1}{-243} = -\frac{1}{243}$

✔ Answer: $-\frac{1}{243}$

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17) $(7)^2 = ?$

- $7 \times 7 = 49$

✔ Answer: 49

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18) $(-4)^4 = ?$

- Even power → positive
- $(-4)^4 = 256$

✔ Answer: 256

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19) $(9)^{-3} = ?$

- $9^{-3} = \frac{1}{9^3} = \frac{1}{729}$

✔ Answer: $\frac{1}{729}$

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20) $(8)^{-3} = ?$

- $8^{-3} = \frac{1}{8^3} = \frac{1}{512}$

✔ Answer: $\frac{1}{512}$

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## ✔ Final Answers:

| # | Answer |
|---|----------------|
| 1 | 64 |
| 2 | 64 |
| 3 | 100 |
| 4 | 1296 |
| 5 | -729 |
| 6 | 100 |
| 7 | 144 |
| 8 | 1296 |
| 9 | 81 |
|10 | $-\frac{1}{128}$ |
|11 | $\frac{1}{256}$ |
|12 | $\frac{1}{81}$ |
|13 | 25 |
|14 | 8 |
|15 | $\frac{1}{144}$ |
|16 | $-\frac{1}{243}$ |
|17 | 49 |
|18 | 256 |
|19 | $\frac{1}{729}$ |
|20 | $\frac{1}{512}$ |

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Let me know if you'd like this in printable format or with steps explained further!