Powers of Exponents (All Positive) (A) - Free Printable

To solve the given problems involving powers of exponents, we will use the Power Rule of exponents, which states:

\[
(a^m)^n = a^{m \cdot n}
\]

This rule tells us that when you have an exponent raised to another exponent, you multiply the exponents.

Let's solve each problem step by step:

---

1. \((9^4)^2\)

Using the Power Rule:
\[
(9^4)^2 = 9^{4 \cdot 2} = 9^8
\]

Answer: \(9^8\)

---

2. \((3^6)^9\)

Using the Power Rule:
\[
(3^6)^9 = 3^{6 \cdot 9} = 3^{54}
\]

Answer: \(3^{54}\)

---

3. \((4^4)^3\)

Using the Power Rule:
\[
(4^4)^3 = 4^{4 \cdot 3} = 4^{12}
\]

Answer: \(4^{12}\)

---

4. \((8^2)^6\)

Using the Power Rule:
\[
(8^2)^6 = 8^{2 \cdot 6} = 8^{12}
\]

Answer: \(8^{12}\)

---

5. \((3^1)^7\)

Using the Power Rule:
\[
(3^1)^7 = 3^{1 \cdot 7} = 3^7
\]

Answer: \(3^7\)

---

6. \((4^6)^8\)

Using the Power Rule:
\[
(4^6)^8 = 4^{6 \cdot 8} = 4^{48}
\]

Answer: \(4^{48}\)

---

7. \((8^1)^2\)

Using the Power Rule:
\[
(8^1)^2 = 8^{1 \cdot 2} = 8^2
\]

Answer: \(8^2\)

---

8. \((7^0)^3\)

First, recall that any number raised to the power of 0 is 1:
\[
7^0 = 1
\]
So:
\[
(7^0)^3 = 1^3 = 1
\]

Answer: \(1\)

---

9. \((6^1)^0\)

First, recall that any non-zero number raised to the power of 0 is 1:
\[
6^1 = 6
\]
So:
\[
(6^1)^0 = 6^0 = 1
\]

Answer: \(1\)

---

10. \((2^6)^7\)

Using the Power Rule:
\[
(2^6)^7 = 2^{6 \cdot 7} = 2^{42}
\]

Answer: \(2^{42}\)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 9^8 \\
2. & 3^{54} \\
3. & 4^{12} \\
4. & 8^{12} \\
5. & 3^7 \\
6. & 4^{48} \\
7. & 8^2 \\
8. & 1 \\
9. & 1 \\
10. & 2^{42} \\
\end{array}
}
\]