Free exponents worksheets - Free Printable

Exponents Worksheet Solution

We will solve each problem step by step, explaining the reasoning behind each calculation.

---

#### 1 a. \( (-7)^1 \times (-3)^3 \)

1. Calculate \( (-7)^1 \):
\[
(-7)^1 = -7
\]

2. Calculate \( (-3)^3 \):
\[
(-3)^3 = (-3) \times (-3) \times (-3) = 9 \times (-3) = -27
\]

3. Multiply the results:
\[
(-7) \times (-27) = 189
\]

Answer:
\[
\boxed{189}
\]

---

#### 1 b. \( 0^{10} \times 0^{22} \)

1. Recall that any number raised to any power is 0 if the base is 0:
\[
0^{10} = 0 \quad \text{and} \quad 0^{22} = 0
\]

2. Multiply the results:
\[
0 \times 0 = 0
\]

Answer:
\[
\boxed{0}
\]

---

#### 2 a. \( 0^{98} - 5^1 \)

1. Calculate \( 0^{98} \):
\[
0^{98} = 0
\]

2. Calculate \( 5^1 \):
\[
5^1 = 5
\]

3. Subtract the results:
\[
0 - 5 = -5
\]

Answer:
\[
\boxed{-5}
\]

---

#### 2 b. \( (-8)^1 + (-1)^2 \)

1. Calculate \( (-8)^1 \):
\[
(-8)^1 = -8
\]

2. Calculate \( (-1)^2 \):
\[
(-1)^2 = (-1) \times (-1) = 1
\]

3. Add the results:
\[
-8 + 1 = -7
\]

Answer:
\[
\boxed{-7}
\]

---

#### 3 a. \( 0^{20} / (-6)^1 \)

1. Calculate \( 0^{20} \):
\[
0^{20} = 0
\]

2. Calculate \( (-6)^1 \):
\[
(-6)^1 = -6
\]

3. Divide the results:
\[
\frac{0}{-6} = 0
\]

Answer:
\[
\boxed{0}
\]

---

#### 3 b. \( 9^2 - (-2)^1 \)

1. Calculate \( 9^2 \):
\[
9^2 = 9 \times 9 = 81
\]

2. Calculate \( (-2)^1 \):
\[
(-2)^1 = -2
\]

3. Subtract the results:
\[
81 - (-2) = 81 + 2 = 83
\]

Answer:
\[
\boxed{83}
\]

---

#### 4 a. \( 7^2 \times (-4)^1 \)

1. Calculate \( 7^2 \):
\[
7^2 = 7 \times 7 = 49
\]

2. Calculate \( (-4)^1 \):
\[
(-4)^1 = -4
\]

3. Multiply the results:
\[
49 \times (-4) = -196
\]

Answer:
\[
\boxed{-196}
\]

---

#### 4 b. \( 100^6 / (-1)^{48} \)

1. Calculate \( 100^6 \):
\[
100^6 = (10^2)^6 = 10^{12}
\]

2. Calculate \( (-1)^{48} \):
\[
(-1)^{48} = 1 \quad \text{(since 48 is even)}
\]

3. Divide the results:
\[
\frac{10^{12}}{1} = 10^{12}
\]

Answer:
\[
\boxed{10^{12}}
\]

---

#### 5 a. \( (-2)^5 \times (-1)^{83} \)

1. Calculate \( (-2)^5 \):
\[
(-2)^5 = (-2) \times (-2) \times (-2) \times (-2) \times (-2) = 32 \times (-2) = -32
\]

2. Calculate \( (-1)^{83} \):
\[
(-1)^{83} = -1 \quad \text{(since 83 is odd)}
\]

3. Multiply the results:
\[
(-32) \times (-1) = 32
\]

Answer:
\[
\boxed{32}
\]

---

#### 5 b. \( 0^{17} \times 0^{68} \)

1. Calculate \( 0^{17} \):
\[
0^{17} = 0
\]

2. Calculate \( 0^{68} \):
\[
0^{68} = 0
\]

3. Multiply the results:
\[
0 \times 0 = 0
\]

Answer:
\[
\boxed{0}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1 \text{ a. } 189 & 1 \text{ b. } 0 \\
2 \text{ a. } -5 & 2 \text{ b. } -7 \\
3 \text{ a. } 0 & 3 \text{ b. } 83 \\
4 \text{ a. } -196 & 4 \text{ b. } 10^{12} \\
5 \text{ a. } 32 & 5 \text{ b. } 0 \\
\end{array}
}
\]