Question

Simplify using the quotient rule of exponents three to the fifth power times three to the fourth power over three to the third power

Answer 1

To simplify the expression \(\frac{3^5 \times 3^4}{3^3}\), we can use the properties of exponents.

1. First, apply the product rule of exponents for the numerator:
\[
3^5 \times 3^4 = 3^{5+4} = 3^9
\]

2. Now, we can rewrite the expression:
\[
\frac{3^9}{3^3}
\]

3. Next, apply the quotient rule of exponents, which states that \(\frac{a^m}{a^n} = a^{m-n}\):
\[
\frac{3^9}{3^3} = 3^{9-3} = 3^6
\]

Thus, the simplified expression is:
\[
3^6
\]