Question

Find an expression equivalent to the one shown below.

(3^3)^5 dived by 3^8

A. 9
B. 3^7
C. 3^23
D. 3^0

Answer 1

can you doble check

Answer 2

To solve the expression \((3^3)^5 \div 3^8\), we'll first simplify the expression.

1. Start with \((3^3)^5\). Using the power of a power property of exponents, we multiply the exponents:
\[
(3^3)^5 = 3^{3 \times 5} = 3^{15}
\]

2. Now, we rewrite the expression:
\[
3^{15} \div 3^8
\]

3. Using the quotient of powers property of exponents, we subtract the exponents:
\[
3^{15 - 8} = 3^7
\]

Thus, the expression simplifies to \(3^7\), which corresponds to option B.

The final answer is:
\[
\boxed{3^7}
\]

Answer 3

Sure! Let's go through the calculations again step by step for the expression \((3^3)^5 \div 3^8\).

1. **Simplify \((3^3)^5\)**:
- Using the rule of exponents \( (a^m)^n = a^{m \cdot n} \):
\[
(3^3)^5 = 3^{3 \cdot 5} = 3^{15}
\]

2. **Set up the division**:
\[
3^{15} \div 3^8
\]

3. **Apply the quotient of powers rule**:
- This rule states that \( \frac{a^m}{a^n} = a^{m-n} \):
\[
3^{15} \div 3^8 = 3^{15 - 8} = 3^7
\]

After verifying each step, we can confidently conclude that the expression simplifies correctly to \(3^7\).

Thus, the final answer is:
\[
\boxed{3^7}
\]

Everything checks out! Thank you for asking for a double check.