\( \begin{array}{ll}\text { c) } \frac{35^{a}-3.5^{a}}{2^{2 a} 7^{a}-3.2^{2 a}} & \text { d) } \frac{3^{a+1} \cdot 4^{a}+5.3^{a+1}}{4^{2 a}-25} \\ \text { e) } \frac{7^{a} \cdot 49-7^{a+2} \cdot 2^{-1}}{2^{-3}, 7^{a}} & \text { f) } \frac{2^{3 a-1}+\frac{3}{2}}{2^{4 a-1}+3.2^{a-1}}\end{array} \)

Simplify the expression by following steps: - step0: Solution: \(\frac{\left(7^{a}\times 49-7^{a+2}\times 2^{-1}\right)}{\left(2^{-3}\times 7^{a}\right)}\) - step1: Remove the parentheses: \(\frac{7^{a}\times 49-7^{a+2}\times 2^{-1}}{2^{-3}\times 7^{a}}\) - step2: Multiply the terms: \(\frac{7^{a+2}-7^{a+2}\times 2^{-1}}{2^{-3}\times 7^{a}}\) - step3: Multiply the terms: \(\frac{7^{a+2}-\frac{1}{2}\times 7^{a+2}}{2^{-3}\times 7^{a}}\) - step4: Rewrite the expression: \(\frac{7^{a+2}-\frac{1}{2}\times 7^{a+2}}{\frac{1}{8}\times 7^{a}}\) - step5: Subtract the terms: \(\frac{\frac{7^{a+2}}{2}}{\frac{1}{8}\times 7^{a}}\) - step6: Rewrite the expression: \(\frac{\frac{7^{a+2}}{2}}{\frac{7^{a}}{8}}\) - step7: Multiply by the reciprocal: \(\frac{7^{a+2}}{2}\times \frac{8}{7^{a}}\) - step8: Reduce the fraction: \(7^{2}\times 4\) - step9: Evaluate the power: \(49\times 4\) - step10: Multiply: \(196\) Calculate or simplify the expression \( (2^(3*a-1) + 3/2)/(2^(4*a-1) + 3*2^(a-1)) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(2^{3a-1}+\frac{3}{2}\right)}{\left(2^{4a-1}+3\times 2^{a-1}\right)}\) - step1: Remove the parentheses: \(\frac{2^{3a-1}+\frac{3}{2}}{2^{4a-1}+3\times 2^{a-1}}\) - step2: Rewrite the expression: \(\frac{\frac{1}{2}\left(2^{a}\right)^{3}+\frac{3}{2}}{\frac{1}{2}\left(2^{a}\right)^{4}+\frac{3}{2}\times 2^{a}}\) - step3: Rewrite the expression: \(\frac{\frac{\left(2^{a}\right)^{3}+3}{2}}{\frac{1}{2}\left(2^{a}\right)^{4}+\frac{3}{2}\times 2^{a}}\) - step4: Rewrite the expression: \(\frac{\frac{\left(2^{a}\right)^{3}+3}{2}}{\frac{\left(2^{a}\right)^{4}+3\times 2^{a}}{2}}\) - step5: Multiply by the reciprocal: \(\frac{\left(2^{a}\right)^{3}+3}{2}\times \frac{2}{\left(2^{a}\right)^{4}+3\times 2^{a}}\) - step6: Rewrite the expression: \(\frac{\left(2^{a}\right)^{3}+3}{2}\times \frac{2}{2^{a}\left(\left(2^{a}\right)^{3}+3\right)}\) - step7: Reduce the fraction: \(1\times \frac{1}{2^{a}}\) - step8: Multiply the terms: \(\frac{1}{2^{a}}\) Calculate or simplify the expression \( (3^(a+1)*4^a + 5*3^(a+1))/(4^(2*a) - 25) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(3^{a+1}\times 4^{a}+5\times 3^{a+1}\right)}{\left(4^{2a}-25\right)}\) - step1: Remove the parentheses: \(\frac{3^{a+1}\times 4^{a}+5\times 3^{a+1}}{4^{2a}-25}\) - step2: Rewrite the expression: \(\frac{3\times 3^{a}\left(2^{a}\right)^{2}+15\times 3^{a}}{\left(2^{a}\right)^{4}-25}\) - step3: Factor the expression: \(\frac{3\times 3^{a}\left(\left(2^{a}\right)^{2}+5\right)}{\left(\left(2^{a}\right)^{2}+5\right)\left(\left(2^{a}\right)^{2}-5\right)}\) - step4: Reduce the fraction: \(\frac{3\times 3^{a}}{\left(2^{a}\right)^{2}-5}\) - step5: Calculate: \(\frac{3^{a+1}}{\left(2^{a}\right)^{2}-5}\) - step6: Calculate: \(\frac{3^{a+1}}{2^{2a}-5}\) Calculate or simplify the expression \( (35^a - 3*5^a)/(2^(2*a)*7^a - 3*2^(2*a)) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(35^{a}-3\times 5^{a}\right)}{\left(2^{2a}\times 7^{a}-3\times 2^{2a}\right)}\) - step1: Remove the parentheses: \(\frac{35^{a}-3\times 5^{a}}{2^{2a}\times 7^{a}-3\times 2^{2a}}\) - step2: Multiply the terms: \(\frac{35^{a}-3\times 5^{a}}{28^{a}-3\times 2^{2a}}\) - step3: Rewrite the expression: \(\frac{5^{a}\times 7^{a}-3\times 5^{a}}{\left(2^{a}\right)^{2}\times 7^{a}-3\left(2^{a}\right)^{2}}\) - step4: Factor the expression: \(\frac{5^{a}\left(7^{a}-3\right)}{\left(2^{a}\right)^{2}\left(7^{a}-3\right)}\) - step5: Reduce the fraction: \(\frac{5^{a}}{\left(2^{a}\right)^{2}}\) - step6: Calculate: \(\frac{5^{a}}{2^{2a}}\) Here are the simplified results for each expression: **c)** \[ \frac{35^{a}-3 \cdot 5^{a}}{2^{2 a} 7^{a}-3 \cdot 2^{2 a}} = \frac{5^{a}}{2^{2a}} \] **d)** \[ \frac{3^{a+1} \cdot 4^{a}+5 \cdot 3^{a+1}}{4^{2 a}-25} = \frac{3^{a+1}}{2^{2a}-5} \] **e)** \[ \frac{7^{a} \cdot 49-7^{a+2} \cdot 2^{-1}}{2^{-3} \cdot 7^{a}} = 196 \] **f)** \[ \frac{2^{3 a-1}+\frac{3}{2}}{2^{4 a-1}+3 \cdot 2^{a-1}} = \frac{1}{2^{a}} \] If you have any further questions or need additional assistance, feel free to ask!