3 years ago

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

Mathematics

1 answer:

BabaBlast [244]3 years ago

8 0

Answer:

ab=1

Step-by-step 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

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