Problem: Solve the given exponents addition problems.
The worksheet contains 10 problems involving the addition of terms with exponents. Let's solve each problem step by step.
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####
Problem 1: \( (-9)^2 + 3^4 \)
1. Calculate \( (-9)^2 \):
\[
(-9)^2 = (-9) \times (-9) = 81
\]
2. Calculate \( 3^4 \):
\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\]
3. Add the results:
\[
(-9)^2 + 3^4 = 81 + 81 = 162
\]
Answer: \( 162 \)
---
####
Problem 2: \( (-9)^2 + (-7)^2 \)
1. Calculate \( (-9)^2 \):
\[
(-9)^2 = (-9) \times (-9) = 81
\]
2. Calculate \( (-7)^2 \):
\[
(-7)^2 = (-7) \times (-7) = 49
\]
3. Add the results:
\[
(-9)^2 + (-7)^2 = 81 + 49 = 130
\]
Answer: \( 130 \)
---
####
Problem 3: \( 10^3 + (-9)^2 \)
1. Calculate \( 10^3 \):
\[
10^3 = 10 \times 10 \times 10 = 1000
\]
2. Calculate \( (-9)^2 \):
\[
(-9)^2 = (-9) \times (-9) = 81
\]
3. Add the results:
\[
10^3 + (-9)^2 = 1000 + 81 = 1081
\]
Answer: \( 1081 \)
---
####
Problem 4: \( 9^3 + (-9)^3 \)
1. Calculate \( 9^3 \):
\[
9^3 = 9 \times 9 \times 9 = 729
\]
2. Calculate \( (-9)^3 \):
\[
(-9)^3 = (-9) \times (-9) \times (-9) = -729
\]
3. Add the results:
\[
9^3 + (-9)^3 = 729 + (-729) = 0
\]
Answer: \( 0 \)
---
####
Problem 5: \( 4^2 + (-6)^3 \)
1. Calculate \( 4^2 \):
\[
4^2 = 4 \times 4 = 16
\]
2. Calculate \( (-6)^3 \):
\[
(-6)^3 = (-6) \times (-6) \times (-6) = -216
\]
3. Add the results:
\[
4^2 + (-6)^3 = 16 + (-216) = 16 - 216 = -200
\]
Answer: \( -200 \)
---
####
Problem 6: \( -9^2 + 3^3 \)
1. Calculate \( -9^2 \):
\[
-9^2 = -(9^2) = -(9 \times 9) = -81
\]
(Note: The negative sign applies after calculating the exponent.)
2. Calculate \( 3^3 \):
\[
3^3 = 3 \times 3 \times 3 = 27
\]
3. Add the results:
\[
-9^2 + 3^3 = -81 + 27 = -54
\]
Answer: \( -54 \)
---
####
Problem 7: \( 4^3 + 8^3 \)
1. Calculate \( 4^3 \):
\[
4^3 = 4 \times 4 \times 4 = 64
\]
2. Calculate \( 8^3 \):
\[
8^3 = 8 \times 8 \times 8 = 512
\]
3. Add the results:
\[
4^3 + 8^3 = 64 + 512 = 576
\]
Answer: \( 576 \)
---
####
Problem 8: \( -3^2 + (-8)^2 \)
1. Calculate \( -3^2 \):
\[
-3^2 = -(3^2) = -(3 \times 3) = -9
\]
(Note: The negative sign applies after calculating the exponent.)
2. Calculate \( (-8)^2 \):
\[
(-8)^2 = (-8) \times (-8) = 64
\]
3. Add the results:
\[
-3^2 + (-8)^2 = -9 + 64 = 55
\]
Answer: \( 55 \)
---
####
Problem 9: \( 8^3 + 2^3 \)
1. Calculate \( 8^3 \):
\[
8^3 = 8 \times 8 \times 8 = 512
\]
2. Calculate \( 2^3 \):
\[
2^3 = 2 \times 2 \times 2 = 8
\]
3. Add the results:
\[
8^3 + 2^3 = 512 + 8 = 520
\]
Answer: \( 520 \)
---
####
Problem 10: \( (-2)^4 + (-0.02)^3 \)
1. Calculate \( (-2)^4 \):
\[
(-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16
\]
2. Calculate \( (-0.02)^3 \):
\[
(-0.02)^3 = (-0.02) \times (-0.02) \times (-0.02) = -0.000008
\]
3. Add the results:
\[
(-2)^4 + (-0.02)^3 = 16 + (-0.000008) = 16 - 0.000008 = 15.999992
\]
Answer: \( 15.999992 \)
---
Final Answers:
\[
\boxed{
\begin{array}{ll}
1. & 162 \\
2. & 130 \\
3. & 1081 \\
4. & 0 \\
5. & -200 \\
6. & -54 \\
7. & 576 \\
8. & 55 \\
9. & 520 \\
10. & 15.999992 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of worksheet for algebra 1.
