Question

a to the power b = b to the power a and if b =9a then find a to the power 4* b to the power 8 ​

Answer 1

Answer:

$given : {a}^{b} = {b}^{a} \\ \: \: \: \: \: \: \: \: \: \: \therefore \: {a}^{ \frac{b}{a} } = b \\ \implies \: {a}^{ \frac{9a}{a} } = b \: \: \: ( \because \: b = 9a) \\ \implies \: {a}^{ 9 } = b....(1) \\ now \\ {a}^{4} \times {b}^{8} = {a}^{4} \times ({{a}^{ 9 }})^{8} \\ ..(from \: equation \: 1) \\ = {a}^{4} \times {{a}^{ 9 \times 8}} \\ = {a}^{4} \times {a}^{72} \\ = {a}^{4 + 72} \\ = {a}^{76} \\ thus \\ \huge \fbox{{a}^{4} \times {b}^{8} = {a}^{76} }$