Question

If x=10^a , y=10^b and x^b.y^a=100.prove that xy=1​

Answer 1

ab=1

Explanation:

Assuming that you meant ab=1

`x=10^(a)\\\\y=10^b\\\\x^b*y^a=100\\\\(10^a)^b*(10^b)^a=100\\\\10^(ab)*10^(ba)=100\\\\10^(ab+ba)=100\\\\10^(2ab)=100\\\\(10^2)^(ab)=100\\\\100^(ab)=100\\\\ab=1`this is because the exponents have to be equal