Question
3^4 cdot 3^3/3^5
Answers
Answered by
GPT-4o mini
To simplify the expression \( \frac{3^4 \cdot 3^3}{3^5} \), we can use the properties of exponents.
1. Combine the terms in the numerator:
\[
3^4 \cdot 3^3 = 3^{4+3} = 3^7
\]
2. Now, we can rewrite the expression as:
\[
\frac{3^7}{3^5}
\]
3. Apply the quotient rule of exponents, which states that \( \frac{a^m}{a^n} = a^{m-n} \):
\[
\frac{3^7}{3^5} = 3^{7-5} = 3^2
\]
4. Finally, calculate \( 3^2 \):
\[
3^2 = 9
\]
Thus, the simplified result is:
\[
\boxed{9}
\]
1. Combine the terms in the numerator:
\[
3^4 \cdot 3^3 = 3^{4+3} = 3^7
\]
2. Now, we can rewrite the expression as:
\[
\frac{3^7}{3^5}
\]
3. Apply the quotient rule of exponents, which states that \( \frac{a^m}{a^n} = a^{m-n} \):
\[
\frac{3^7}{3^5} = 3^{7-5} = 3^2
\]
4. Finally, calculate \( 3^2 \):
\[
3^2 = 9
\]
Thus, the simplified result is:
\[
\boxed{9}
\]