Answer:
Question a:
[tex]\frac{(2^3)^6 \times 9^3}{4^2 \times 27}\\= \frac{2^{18} \times 3^6}{2^4 \times 3^3}\\=2^{14} \times 3^3[/tex]
Question b:
[tex]\frac{35 \times 7^3}{5^2 \times 343}\\= \frac{7 \times 5^1 \times 7^3}{5^2 \times 7^3}\\= \frac{5^1 \times 7^4}{5^2 \times 7^3}\\=\frac{7^1}{5^1} = \frac{7}{5}[/tex]
Question c:
Note that this one is particularily simple as anything to the power of zero is equal to 1
[tex]((\frac{2^4 \times 3^6}{12^2})^0)^3\\= 1^3\\ =1[/tex]
Question d:
[tex]\frac{13^3 \times 7^0}{((65 \times 49)^2)^1}\\\frac{13^3}{(65 \times 49)^2}\\\frac{13^3}{(13 \times 5 \times 49)^2}\\\frac{13^3}{13^2 \times 5^2 \times 7^4}\\\frac{13}{5^2 \times 7^4}[/tex]
