SOLUTION: If (a^2 a^3)^x = a^125 and (a^y)^y = a^16/25 where x > 1 and y > 0, what is the product of x and y? (a) 8/5 (b) 4 (c) 8 (d) 16 (e) 20

Algebra ->  Exponents -> SOLUTION: If (a^2 a^3)^x = a^125 and (a^y)^y = a^16/25 where x > 1 and y > 0, what is the product of x and y? (a) 8/5 (b) 4 (c) 8 (d) 16 (e) 20       Log On


   

Question 340312: If (a^2 a^3)^x = a^125 and (a^y)^y = a^16/25 where x > 1 and y > 0, what is the product of x and y?
(a) 8/5 (b) 4 (c) 8 (d) 16 (e) 20
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%5E2+a%5E3%29%5Ex+=+a%5E125
%28a%5E%282%2B3%29%29%5Ex+=+a%5E125
%28a%5E5%29%5Ex+=+a%5E125
a%5E%285x%29+=+a%5E125
5x=125
highlight%28x=25%29
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.
.
+%28a%5Ey%29%5Ey+=+a%5E16%2F25
a%5E%28y%5E2%29=a%5E%2816%2F25%29
y%5E2=16%2F25
y=0+%2B-+4%2F5
You also know that y%3E0, so then
highlight%28y=4%2F5%29
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.
.
xy=25%284%2F5%29
highlight_green%28xy=20%29