Free exponents worksheets - Free Printable

Explanation:
Let’s solve each problem one by one, using basic exponent rules:

Rule reminders:
- Any number (except 0) to the power of 1 is itself: $ a^1 = a $
- Zero to any positive power is 0: $ 0^n = 0 $ for $ n > 0 $
- Any non-zero number to the power of 0 is 1: $ a^0 = 1 $ (but not needed here)
- A negative base raised to an even exponent becomes positive.
- A negative base raised to an odd exponent stays negative.
- $ a^n $ means multiply $ a $ by itself $ n $ times.

Now go through each:

1. a. $ 0^{17} $ → 0 multiplied by itself 17 times = 0
b. $ 10^4 = 10 \times 10 \times 10 \times 10 = 10{,}000 $

2. a. $ 5^2 = 5 \times 5 = 25 $
b. $ (-10)^7 $: odd exponent → stays negative; $ 10^7 = 10{,}000{,}000 $, so answer = –10,000,000

3. a. $ 7^2 = 7 \times 7 = 49 $
b. $ (-4)^1 = -4 $

4. a. $ (-100)^6 $: even exponent → positive; $ 100^6 = (10^2)^6 = 10^{12} = 1{,}000{,}000{,}000{,}000 $
So answer = 1,000,000,000,000
b. $ (-4)^3 = (-4) \times (-4) \times (-4) = 16 \times (-4) = -64 $

5. a. $ 1^{47} = 1 $ (1 to any power is 1)
b. $ (-2)^6 $: even exponent → positive; $ 2^6 = 64 $, so answer = 64

6. a. $ 5^3 = 5 \times 5 \times 5 = 125 $
b. $ (-8)^1 = -8 $

7. a. $ (-3)^3 = (-3) \times (-3) \times (-3) = 9 \times (-3) = -27 $
b. $ 7^1 = 7 $

8. a. $ 0^4 = 0 $
b. $ (-3)^1 = -3 $

9. a. $ 100^3 = 100 \times 100 \times 100 = 1{,}000{,}000 $
b. $ 0^{23} = 0 $ (since exponent > 0)

10. a. $ (-9)^1 = -9 $
b. $ 0^{36} = 0 $

Let me double-check a few tricky ones:
- $ (-100)^6 $: yes, even exponent → positive; $ 100^6 = (10^2)^6 = 10^{12} $ → correct.
- $ (-4)^3 = -64 $: yes, $ 4^3 = 64 $, sign negative → correct.
- All zeros with positive exponents are 0 — correct.
- All powers of 1 are 1 — correct.

Everything checks out.

Final Answer:
1 a. 0
1 b. 10000
2 a. 25
2 b. –10000000
3 a. 49
3 b. –4
4 a. 1000000000000
4 b. –64
5 a. 1
5 b. 64
6 a. 125
6 b. –8
7 a. –27
7 b. 7
8 a. 0
8 b. –3
9 a. 1000000
9 b. 0
10 a. –9
10 b. 0