Exponents Worksheets with Answer Key - Free Printable

Exponents Worksheet Solution

The worksheet involves solving basic exponent problems. Here is the step-by-step solution for each problem:

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#### 1 a. \( 2^1 \)
- Any number raised to the power of 1 is the number itself.
- \( 2^1 = 2 \)

Answer: \( 2 \)

#### 1 b. \( 5^2 \)
- \( 5^2 \) means \( 5 \times 5 \).
- \( 5 \times 5 = 25 \)

Answer: \( 25 \)

#### 2 a. \( 3^3 \)
- \( 3^3 \) means \( 3 \times 3 \times 3 \).
- \( 3 \times 3 = 9 \)
- \( 9 \times 3 = 27 \)

Answer: \( 27 \)

#### 2 b. \( 8^2 \)
- \( 8^2 \) means \( 8 \times 8 \).
- \( 8 \times 8 = 64 \)

Answer: \( 64 \)

#### 3 a. \( 0^{82} \)
- Any number (except 0) raised to any power is 0.
- \( 0^{82} = 0 \)

Answer: \( 0 \)

#### 3 b. \( 100^1 \)
- Any number raised to the power of 1 is the number itself.
- \( 100^1 = 100 \)

Answer: \( 100 \)

#### 4 a. \( 10^7 \)
- \( 10^7 \) means multiplying 10 by itself 7 times.
- \( 10^7 = 10,000,000 \)

Answer: \( 10,000,000 \)

#### 4 b. \( 0^{20} \)
- Any number (except 0) raised to any power is 0.
- \( 0^{20} = 0 \)

Answer: \( 0 \)

#### 5 a. \( 8^1 \)
- Any number raised to the power of 1 is the number itself.
- \( 8^1 = 8 \)

Answer: \( 8 \)

#### 5 b. \( 5^1 \)
- Any number raised to the power of 1 is the number itself.
- \( 5^1 = 5 \)

Answer: \( 5 \)

#### 6 a. \( 10^4 \)
- \( 10^4 \) means multiplying 10 by itself 4 times.
- \( 10^4 = 10,000 \)

Answer: \( 10,000 \)

#### 6 b. \( 6^2 \)
- \( 6^2 \) means \( 6 \times 6 \).
- \( 6 \times 6 = 36 \)

Answer: \( 36 \)

#### 7 a. \( 4^2 \)
- \( 4^2 \) means \( 4 \times 4 \).
- \( 4 \times 4 = 16 \)

Answer: \( 16 \)

#### 7 b. \( 7^2 \)
- \( 7^2 \) means \( 7 \times 7 \).
- \( 7 \times 7 = 49 \)

Answer: \( 49 \)

#### 8 a. \( 100^6 \)
- \( 100^6 \) means multiplying 100 by itself 6 times.
- \( 100^6 = 1,000,000,000,000 \) (1 followed by 12 zeros)

Answer: \( 1,000,000,000,000 \)

#### 8 b. \( 1^9 \)
- Any number raised to any power is 1 if the base is 1.
- \( 1^9 = 1 \)

Answer: \( 1 \)

#### 9 a. \( 9^2 \)
- \( 9^2 \) means \( 9 \times 9 \).
- \( 9 \times 9 = 81 \)

Answer: \( 81 \)

#### 9 b. \( 1^{99} \)
- Any number raised to any power is 1 if the base is 1.
- \( 1^{99} = 1 \)

Answer: \( 1 \)

#### 10 a. \( 100^2 \)
- \( 100^2 \) means \( 100 \times 100 \).
- \( 100 \times 100 = 10,000 \)

Answer: \( 10,000 \)

#### 10 b. \( 2^3 \)
- \( 2^3 \) means \( 2 \times 2 \times 2 \).
- \( 2 \times 2 = 4 \)
- \( 4 \times 2 = 8 \)

Answer: \( 8 \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1 \text{ a. } 2 & 1 \text{ b. } 25 \\
2 \text{ a. } 27 & 2 \text{ b. } 64 \\
3 \text{ a. } 0 & 3 \text{ b. } 100 \\
4 \text{ a. } 10,000,000 & 4 \text{ b. } 0 \\
5 \text{ a. } 8 & 5 \text{ b. } 5 \\
6 \text{ a. } 10,000 & 6 \text{ b. } 36 \\
7 \text{ a. } 16 & 7 \text{ b. } 49 \\
8 \text{ a. } 1,000,000,000,000 & 8 \text{ b. } 1 \\
9 \text{ a. } 81 & 9 \text{ b. } 1 \\
10 \text{ a. } 10,000 & 10 \text{ b. } 8 \\
\end{array}
}
\]