Let's solve each part of the problem step-by-step.
### First Expression: [tex]\(4^7 \div 4^4\)[/tex]
1. Rewrite the Division of Exponents: When dividing exponential terms with the same base, you can subtract the exponents.
[tex]\[
4^7 \div 4^4 = 4^{7-4}
\][/tex]
2. Simplify the Exponent:
[tex]\[
4^{7-4} = 4^3
\][/tex]
3. Calculate [tex]\(4^3\)[/tex]:
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
So, [tex]\(4^7 \div 4^4 = 64\)[/tex].
### Second Expression: [tex]\(3^5 \div 3^2\)[/tex]
1. Rewrite the Division of Exponents: Similarly, when dividing exponential terms with the same base, you subtract the exponents.
[tex]\[
3^5 \div 3^2 = 3^{5-2}
\][/tex]
2. Simplify the Exponent:
[tex]\[
3^{5-2} = 3^3
\][/tex]
3. Calculate [tex]\(3^3\)[/tex]:
[tex]\[
3^3 = 3 \times 3 \times 3 = 27
\][/tex]
So, [tex]\(3^5 \div 3^2 = 27\)[/tex].
In summary:
[tex]\[
4^7 \div 4^4 = 64
\][/tex]
[tex]\[
3^5 \div 3^2 = 27
\][/tex]
