Algebra 1 Worksheets | Exponents Worksheets - Free Printable

Of course! Let's solve each problem step by step and explain the reasoning.

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Evaluate to a single number.

1. $3^3 + 5^2$

- $3^3 = 3 \times 3 \times 3 = 27$
- $5^2 = 5 \times 5 = 25$
- Add: $27 + 25 = 52$

✔ Answer: 52

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2. $4^4 + 6^3$

- $4^4 = 4 \times 4 \times 4 \times 4 = 256$
- $6^3 = 6 \times 6 \times 6 = 216$
- Add: $256 + 216 = 472$

✔ Answer: 472

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3. $7^3 + 5^4$

- $7^3 = 7 \times 7 \times 7 = 343$
- $5^4 = 5 \times 5 \times 5 \times 5 = 625$
- Add: $343 + 625 = 968$

✔ Answer: 968

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Simplify.

4. $-4^3 \times 3^4$

⚠️ Important: The negative sign is *not* part of the base unless parentheses are used. So this means $-(4^3) \times 3^4$, not $(-4)^3$.

- $4^3 = 64$, so $-4^3 = -64$
- $3^4 = 81$
- Multiply: $-64 \times 81 = -5184$

✔ Answer: -5184

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5. $8^4 \times 3^{-2}$

- $8^4 = (2^3)^4 = 2^{12} = 4096$
*(or just calculate: $8 \times 8 \times 8 \times 8 = 4096$)*
- $3^{-2} = \frac{1}{3^2} = \frac{1}{9}$
- Multiply: $4096 \times \frac{1}{9} = \frac{4096}{9}$

✔ Answer: $\frac{4096}{9}$ (or as a mixed number: $455 \frac{1}{9}$)

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6. $6^{-3} \times 4^{-3}$

Use exponent rule: $a^{-n} \times b^{-n} = (a \times b)^{-n}$

So:
- $6^{-3} \times 4^{-3} = (6 \times 4)^{-3} = 24^{-3} = \frac{1}{24^3}$

Now compute $24^3$:
- $24^2 = 576$
- $24^3 = 576 \times 24 = 13,824$

✔ Answer: $\frac{1}{13824}$

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Simplify (with variables).

7. $(8x)^0(12x)^3$

Any non-zero expression to the power of 0 is 1.
- $(8x)^0 = 1$ (as long as $x \neq 0$, which we assume)
- $(12x)^3 = 12^3 \cdot x^3 = 1728x^3$
- Multiply: $1 \times 1728x^3 = 1728x^3$

✔ Answer: $1728x^3$

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8. $(12x)^2(13x)^2$

Use exponent rule: $(ab)^n = a^n b^n$, and also $a^m \cdot b^m = (ab)^m$

So:
- $(12x)^2 = 144x^2$
- $(13x)^2 = 169x^2$
- Multiply: $144x^2 \cdot 169x^2 = (144 \cdot 169) \cdot x^{4}$

Calculate $144 \times 169$:

You can do:
- $144 \times 170 = 144 \times (100 + 70) = 14400 + 10080 = 24480$
- Subtract $144 \times 1 = 144$ → $24480 - 144 = 24336$

Or use $(12 \cdot 13)^2 \cdot x^4 = (156)^2 x^4$

$156^2 = (150 + 6)^2 = 150^2 + 2\cdot150\cdot6 + 6^2 = 22500 + 1800 + 36 = 24336$

✔ Answer: $24336x^4$

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9. $(21x)^2(14x)^3$

Break it down:
- $(21x)^2 = 21^2 \cdot x^2 = 441x^2$
- $(14x)^3 = 14^3 \cdot x^3 = 2744x^3$
- Multiply: $441x^2 \cdot 2744x^3 = (441 \cdot 2744) \cdot x^5$

Let’s compute $441 \cdot 2744$:

Note: $441 = 21^2$, $2744 = 14^3 = (2 \cdot 7)^3 = 8 \cdot 343$

Alternatively, factor:
- $441 = 9 \cdot 49 = 9 \cdot 7^2$
- $2744 = 8 \cdot 343 = 8 \cdot 7^3$
→ Total: $9 \cdot 8 \cdot 7^5 = 72 \cdot 16807 = ?$

Better to multiply directly or use calculator in mind:

But since this is a worksheet, perhaps they expect simplification without full multiplication? Actually, let’s compute:

$441 \times 2744$

Break 2744 into 2000 + 700 + 40 + 4:

- $441 × 2000 = 882,000$
- $441 × 700 = 308,700$
- $441 × 40 = 17,640$
- $441 × 4 = 1,764$

Add them:

882,000
+308,700 = 1,190,700
+17,640 = 1,208,340
+1,764 = 1,210,104

So total coefficient is 1,210,104

✔ Answer: $1,210,104x^5$

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10. $(34x)^2(19x)^3$

Same approach:

- $(34x)^2 = 34^2 x^2 = 1156x^2$
- $(19x)^3 = 19^3 x^3 = 6859x^3$
- Multiply: $1156 \cdot 6859 \cdot x^5$

Compute $1156 × 6859$ — this is big!

We can leave it as is for now, but let’s try to compute:

Actually, note that $1156 = 34^2$, $6859 = 19^3$, so total = $34^2 \cdot 19^3 \cdot x^5$

But if you must multiply:

Use approximation or calculator — but since this is a worksheet, maybe they expect the simplified form with exponents? But instructions say "simplify", which usually means combine like terms and compute coefficients.

Let me compute:

First, $1156 × 6859$

Break 6859 = 6000 + 800 + 50 + 9

- $1156 × 6000 = 6,936,000$
- $1156 × 800 = 924,800$
- $1156 × 50 = 57,800$
- $1156 × 9 = 10,404$

Add:

6,936,000
+924,800 = 7,860,800
+57,800 = 7,918,600
+10,404 = 7,929,004

✔ Answer: $7,929,004x^5$

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11. $f(x) = (-2x)^2 ÷ (4x)$

First, simplify numerator: $(-2x)^2 = (-2)^2 \cdot x^2 = 4x^2$

Then divide by $4x$: $\frac{4x^2}{4x} = \frac{4}{4} \cdot \frac{x^2}{x} = 1 \cdot x = x$

✔ Answer: $x$

*(Note: This is valid only when $x \ne 0$, since division by zero is undefined.)*

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12. $f(x) = (22x)^0 ÷ (11x)^2$

- $(22x)^0 = 1$ (again, assuming $x \ne 0$)
- $(11x)^2 = 121x^2$
- So: $\frac{1}{121x^2}$

✔ Answer: $\frac{1}{121x^2}$

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## ✔ Final Answers Summary:

1. 52
2. 472
3. 968
4. -5184
5. $\frac{4096}{9}$
6. $\frac{1}{13824}$
7. $1728x^3$
8. $24336x^4$
9. $1,210,104x^5$
10. $7,929,004x^5$
11. $x$
12. $\frac{1}{121x^2}$

Let me know if you’d like these written out in a printable format or need help with similar problems!