Sure! Let's simplify each expression step-by-step.
### Part (a)
Simplify [tex]\(4^9 \times 4^3\)[/tex]:
1. When multiplying powers with the same base, you add the exponents:
[tex]\[
4^9 \times 4^3 = 4^{9+3}
\][/tex]
2. Adding the exponents, we get:
[tex]\[
4^{9+3} = 4^{12}
\][/tex]
3. Calculating [tex]\(4^{12}\)[/tex], we find:
[tex]\[
4^{12} = 16777216
\][/tex]
So, [tex]\(4^9 \times 4^3 = 16777216\)[/tex].
---
### Part (b)
Simplify [tex]\(6^5 \times 6^2\)[/tex]:
1. When multiplying powers with the same base, you add the exponents:
[tex]\[
6^5 \times 6^2 = 6^{5+2}
\][/tex]
2. Adding the exponents, we get:
[tex]\[
6^{5+2} = 6^{7}
\][/tex]
3. Calculating [tex]\(6^{7}\)[/tex], we find:
[tex]\[
6^{7} = 279936
\][/tex]
So, [tex]\(6^5 \times 6^2 = 279936\)[/tex].
---
### Part (c)
Simplify [tex]\(8^6 \div 8\)[/tex]:
1. When dividing powers with the same base, you subtract the exponents:
[tex]\[
8^6 \div 8 = 8^{6-1}
\][/tex]
2. Subtracting the exponents, we get:
[tex]\[
8^{6-1} = 8^{5}
\][/tex]
3. Calculating [tex]\(8^{5}\)[/tex], we find:
[tex]\[
8^{5} = 32768
\][/tex]
So, [tex]\(8^6 \div 8 = 32768\)[/tex].
---
### Part (d)
Simplify [tex]\(7^8 \div 7^6\)[/tex]:
1. When dividing powers with the same base, you subtract the exponents:
[tex]\[
7^8 \div 7^6 = 7^{8-6}
\][/tex]
2. Subtracting the exponents, we get:
[tex]\[
7^{8-6} = 7^{2}
\][/tex]
3. Calculating [tex]\(7^{2}\)[/tex], we find:
[tex]\[
7^{2} = 49
\][/tex]
So, [tex]\(7^8 \div 7^6 = 49\)[/tex].
---
Therefore, the simplified results are:
a) [tex]\(4^9 \times 4^3 = 16777216\)[/tex]
b) [tex]\(6^5 \times 6^2 = 279936\)[/tex]
c) [tex]\(8^6 \div 8 = 32768\)[/tex]
d) [tex]\(7^8 \div 7^6 = 49\)[/tex]
