Exponent Multiplication Worksheets - 15 Worksheets Library - Free Printable

Explanation:
We are multiplying two powers that have the same base. The rule is:

> When multiplying powers with the same base, add the exponents:
> $ a^m \times a^n = a^{m+n} $

Let’s go through each problem one by one and apply this rule.

1) $ 2^3 \times 2^2 = 2^{3+2} = 2^5 = 32 $
2) $ 3^4 \times 3^2 = 3^{4+2} = 3^6 = 729 $
3) $ 5^2 \times 5^7 = 5^{2+7} = 5^9 = 1,953,125 $
4) $ 4^3 \times 4^1 = 4^{3+1} = 4^4 = 256 $
5) $ 3^4 \times 3^7 = 3^{4+7} = 3^{11} = 177,147 $
6) $ 6^2 \times 6^3 = 6^{2+3} = 6^5 = 7,776 $
7) $ 7^0 \times 7^4 = 7^{0+4} = 7^4 = 2,401 $
*(Remember: any number to the 0 power is 1, so $7^0 = 1$)*
8) $ 2^3 \times 2^6 = 2^{3+6} = 2^9 = 512 $
9) $ 8^{12} \times 8^3 = 8^{12+3} = 8^{15} $ — but we can leave it as $8^{15}$ unless asked for the full number (it's huge). However, the instruction says *“Write the answer as a single exponent”*, so we just write the exponent form.
10) $ 10^4 \times 10^1 = 10^{4+1} = 10^5 $

Now continue with the rest:

11) $ 8^2 \times 8^7 = 8^{2+7} = 8^9 $
12) $ 12^3 \times 12^4 = 12^{3+4} = 12^7 $
13) $ 4^2 \times 4^7 = 4^{2+7} = 4^9 $
14) $ 6^3 \times 6^5 = 6^{3+5} = 6^8 $
15) $ 5^2 \times 5^7 = 5^{2+7} = 5^9 $ *(same as #3)*
16) $ 9^3 \times 9^0 = 9^{3+0} = 9^3 = 729 $
17) $ 5^3 \times 5^4 = 5^{3+4} = 5^7 = 78,125 $
18) $ 8^3 \times 8^7 = 8^{3+7} = 8^{10} $
19) $ 6^3 \times 6^6 = 6^{3+6} = 6^9 $
20) $ 3^7 \times 3^4 = 3^{7+4} = 3^{11} $ *(same as #5)*

But wait — the instructions say:
“Write the answer as a single exponent.”

That means we should give answers like $2^5$, $3^6$, etc., not the expanded number — unless the exponent simplifies to something small and they expect the value? Let’s double-check the wording:

> Multiply the exponents with the same base and Write the answer as a single exponent.

Yes — “as a single exponent” means express as one power, e.g., $2^5$, not 32.

So for all problems, we only need to combine exponents — no need to compute the final number.

Let me rewrite all answers in exponent form only:

1) $2^{5}$
2) $3^{6}$
3) $5^{9}$
4) $4^{4}$
5) $3^{11}$
6) $6^{5}$
7) $7^{4}$
8) $2^{9}$
9) $8^{15}$
10) $10^{5}$
11) $8^{9}$
12) $12^{7}$
13) $4^{9}$
14) $6^{8}$
15) $5^{9}$
16) $9^{3}$
17) $5^{7}$
18) $8^{10}$
19) $6^{9}$
20) $3^{11}$

Double-check each addition:
1) 3+2=5 ✔
2) 4+2=6 ✔
3) 2+7=9 ✔
4) 3+1=4 ✔
5) 4+7=11 ✔
6) 2+3=5 ✔
7) 0+4=4 ✔
8) 3+6=9 ✔
9) 12+3=15 ✔
10) 4+1=5 ✔
11) 2+7=9 ✔
12) 3+4=7 ✔
13) 2+7=9 ✔
14) 3+5=8 ✔
15) 2+7=9 ✔
16) 3+0=3 ✔
17) 3+4=7 ✔
18) 3+7=10 ✔
19) 3+6=9 ✔
20) 7+4=11 ✔

All correct.

Final Answer:
1) $2^5$
2) $3^6$
3) $5^9$
4) $4^4$
5) $3^{11}$
6) $6^5$
7) $7^4$
8) $2^9$
9) $8^{15}$
10) $10^5$
11) $8^9$
12) $12^7$
13) $4^9$
14) $6^8$
15) $5^9$
16) $9^3$
17) $5^7$
18) $8^{10}$
19) $6^9$
20) $3^{11}$