Sure! Let's simplify the given expression step-by-step:
We are given:
[tex]\[
\frac{3^5 \times 3^7}{3^3 \times 3^4}
\][/tex]
First, apply the properties of exponents. The property [tex]\(a^m \times a^n = a^{m+n}\)[/tex] allows us to combine the exponents in the numerator and the denominator:
For the numerator:
[tex]\[
3^5 \times 3^7 = 3^{5+7} = 3^{12}
\][/tex]
For the denominator:
[tex]\[
3^3 \times 3^4 = 3^{3+4} = 3^7
\][/tex]
Next, we simplify the division of exponents. According to the property [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex]:
[tex]\[
\frac{3^{12}}{3^7} = 3^{12-7} = 3^5
\][/tex]
So, the simplified form of the expression is:
[tex]\[
3^5
\][/tex]
Thus, the final answer is:
[tex]\[
3^5
\][/tex]
