Exponents Worksheets | Worksheets Worksheets - Free Printable

Problem: Solve the given worksheet on exponents.

The worksheet consists of two sections:
1. Evaluate to a single number (Questions 1–6).
2. Simplify (Questions 7–12).

Let's solve each question step by step.

---

Section 1: Evaluate to a single number

#### Question 1: \( 3^2 + 5^2 \)
- Calculate \( 3^2 \):
\[
3^2 = 3 \times 3 = 9
\]
- Calculate \( 5^2 \):
\[
5^2 = 5 \times 5 = 25
\]
- Add the results:
\[
3^2 + 5^2 = 9 + 25 = 34
\]

Answer: \( 34 \)

#### Question 2: \( 4^3 + 6^2 \)
- Calculate \( 4^3 \):
\[
4^3 = 4 \times 4 \times 4 = 64
\]
- Calculate \( 6^2 \):
\[
6^2 = 6 \times 6 = 36
\]
- Add the results:
\[
4^3 + 6^2 = 64 + 36 = 100
\]

Answer: \( 100 \)

#### Question 3: \( 7^2 + 5^3 \)
- Calculate \( 7^2 \):
\[
7^2 = 7 \times 7 = 49
\]
- Calculate \( 5^3 \):
\[
5^3 = 5 \times 5 \times 5 = 125
\]
- Add the results:
\[
7^2 + 5^3 = 49 + 125 = 174
\]

Answer: \( 174 \)

#### Question 4: \( -4^2 \times 3^2 \)
- Calculate \( 4^2 \):
\[
4^2 = 4 \times 4 = 16
\]
- Note that the negative sign is not part of the exponentiation, so:
\[
-4^2 = -(4^2) = -16
\]
- Calculate \( 3^2 \):
\[
3^2 = 3 \times 3 = 9
\]
- Multiply the results:
\[
-4^2 \times 3^2 = -16 \times 9 = -144
\]

Answer: \( -144 \)

#### Question 5: \( 8^2 \times 3^2 \)
- Calculate \( 8^2 \):
\[
8^2 = 8 \times 8 = 64
\]
- Calculate \( 3^2 \):
\[
3^2 = 3 \times 3 = 9
\]
- Multiply the results:
\[
8^2 \times 3^2 = 64 \times 9 = 576
\]

Answer: \( 576 \)

#### Question 6: \( 6^2 \times 4^3 \)
- Calculate \( 6^2 \):
\[
6^2 = 6 \times 6 = 36
\]
- Calculate \( 4^3 \):
\[
4^3 = 4 \times 4 \times 4 = 64
\]
- Multiply the results:
\[
6^2 \times 4^3 = 36 \times 64 = 2304
\]

Answer: \( 2304 \)

---

Section 2: Simplify

#### Question 7: \( (8x)^0 \times (12x)^3 \)
- Any non-zero number raised to the power of 0 is 1:
\[
(8x)^0 = 1
\]
- Simplify \( (12x)^3 \):
\[
(12x)^3 = 12^3 \times x^3 = (12 \times 12 \times 12) \times x^3 = 1728x^3
\]
- Multiply the results:
\[
(8x)^0 \times (12x)^3 = 1 \times 1728x^3 = 1728x^3
\]

Answer: \( 1728x^3 \)

#### Question 8: \( (12x^2)(13x^3) \)
- Multiply the coefficients:
\[
12 \times 13 = 156
\]
- Add the exponents of \( x \):
\[
x^2 \times x^3 = x^{2+3} = x^5
\]
- Combine the results:
\[
(12x^2)(13x^3) = 156x^5
\]

Answer: \( 156x^5 \)

#### Question 9: \( (21x^2)(14x^3) \)
- Multiply the coefficients:
\[
21 \times 14 = 294
\]
- Add the exponents of \( x \):
\[
x^2 \times x^3 = x^{2+3} = x^5
\]
- Combine the results:
\[
(21x^2)(14x^3) = 294x^5
\]

Answer: \( 294x^5 \)

#### Question 10: \( (3x^2)(13x^3) \)
- Multiply the coefficients:
\[
3 \times 13 = 39
\]
- Add the exponents of \( x \):
\[
x^2 \times x^3 = x^{2+3} = x^5
\]
- Combine the results:
\[
(3x^2)(13x^3) = 39x^5
\]

Answer: \( 39x^5 \)

#### Question 11: \( (-2x)^3 \times (4x) \)
- Simplify \( (-2x)^3 \):
\[
(-2x)^3 = (-2)^3 \times x^3 = (-8) \times x^3 = -8x^3
\]
- Multiply by \( 4x \):
\[
(-8x^3)(4x) = (-8 \times 4) \times (x^3 \times x) = -32x^{3+1} = -32x^4
\]

Answer: \( -32x^4 \)

#### Question 12: \( (2x)^3 \times (11x^2) \)
- Simplify \( (2x)^3 \):
\[
(2x)^3 = 2^3 \times x^3 = 8x^3
\]
- Multiply by \( 11x^2 \):
\[
(8x^3)(11x^2) = (8 \times 11) \times (x^3 \times x^2) = 88x^{3+2} = 88x^5
\]

Answer: \( 88x^5 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 34 \\
2. & 100 \\
3. & 174 \\
4. & -144 \\
5. & 576 \\
6. & 2304 \\
7. & 1728x^3 \\
8. & 156x^5 \\
9. & 294x^5 \\
10. & 39x^5 \\
11. & -32x^4 \\
12. & 88x^5 \\
\end{array}
}
\]