Exponents Worksheets - free & printable | Worsheets library - Free Printable

Here's the step-by-step solution for each problem on the Exponents Worksheet.

---

1 a. \(\left(\frac{2}{3}\right)^2 \div \left(\frac{1}{2}\right)^6\)

- First, compute each exponent:
- \(\left(\frac{2}{3}\right)^2 = \frac{4}{9}\)
- \(\left(\frac{1}{2}\right)^6 = \frac{1}{64}\)

- Now divide:
\(\frac{4}{9} \div \frac{1}{64} = \frac{4}{9} \times \frac{64}{1} = \frac{256}{9}\)

✔ Answer: \(\frac{256}{9}\) (or \(28 \frac{4}{9}\) as a mixed number)

---

1 b. \(\left(\frac{5}{7}\right)^2 \times \left(\frac{5}{7}\right)^1\)

- When multiplying same bases, add exponents:
- \(\left(\frac{5}{7}\right)^{2+1} = \left(\frac{5}{7}\right)^3 = \frac{125}{343}\)

✔ Answer: \(\frac{125}{343}\)

---

2 a. \(0.6^1 \times 0.2^3\)

- Compute each part:
- \(0.6^1 = 0.6\)
- \(0.2^3 = 0.2 \times 0.2 \times 0.2 = 0.008\)

- Multiply:
\(0.6 \times 0.008 = 0.0048\)

✔ Answer: \(0.0048\)

---

2 b. \(\left(\frac{2}{5}\right)^3 \times \left(\frac{2}{5}\right)^2\)

- Same base → add exponents:
\(\left(\frac{2}{5}\right)^{3+2} = \left(\frac{2}{5}\right)^5 = \frac{32}{3125}\)

✔ Answer: \(\frac{32}{3125}\)

---

3 a. \(1^{99} - 0.6^2\)

- Any power of 1 is 1: \(1^{99} = 1\)
- \(0.6^2 = 0.36\)
- Subtract: \(1 - 0.36 = 0.64\)

✔ Answer: \(0.64\)

---

3 b. \(0.2^1 \times \left(\frac{1}{8}\right)^2\)

- \(0.2^1 = 0.2\)
- \(\left(\frac{1}{8}\right)^2 = \frac{1}{64}\)
- Multiply: \(0.2 \times \frac{1}{64} = \frac{1}{5} \times \frac{1}{64} = \frac{1}{320}\)

✔ Answer: \(\frac{1}{320}\) (or 0.003125 as decimal)

---

4 a. \(\left(\frac{1}{2}\right)^2 \div \left(\frac{5}{8}\right)^1\)

- \(\left(\frac{1}{2}\right)^2 = \frac{1}{4}\)
- \(\left(\frac{5}{8}\right)^1 = \frac{5}{8}\)
- Divide: \(\frac{1}{4} \div \frac{5}{8} = \frac{1}{4} \times \frac{8}{5} = \frac{8}{20} = \frac{2}{5}\)

✔ Answer: \(\frac{2}{5}\) (or 0.4)

---

4 b. \(7^2 - 0.5^3\)

- \(7^2 = 49\)
- \(0.5^3 = 0.125\)
- Subtract: \(49 - 0.125 = 48.875\)

✔ Answer: \(48.875\) (or \(48 \frac{7}{8}\))

---

5 a. \(3^1 \div 0.8^2\)

- \(3^1 = 3\)
- \(0.8^2 = 0.64\)
- Divide: \(3 \div 0.64 = \frac{3}{0.64} = \frac{300}{64} = \frac{75}{16} = 4.6875\)

✔ Answer: \(\frac{75}{16}\) or 4.6875

---

5 b. \(0.7^2 + 0.9^1\)

- \(0.7^2 = 0.49\)
- \(0.9^1 = 0.9\)
- Add: \(0.49 + 0.9 = 1.39\)

✔ Answer: \(1.39\)

---

## ✔ Final Answers Summary:

| Problem | Answer |
|---------|--------------------|
| 1a | \(\frac{256}{9}\) |
| 1b | \(\frac{125}{343}\) |
| 2a | \(0.0048\) |
| 2b | \(\frac{32}{3125}\) |
| 3a | \(0.64\) |
| 3b | \(\frac{1}{320}\) |
| 4a | \(\frac{2}{5}\) |
| 4b | \(48.875\) |
| 5a | \(\frac{75}{16}\) or \(4.6875\) |
| 5b | \(1.39\) |

Let me know if you want these in different forms (fractions, decimals, mixed numbers) or need more explanation!