If `(a^(x^(2)))/(a^(x^(2)-y^(2)))=a^(4) and ygt0`, what is the value of y?

Options

A. `0`
B. `1`
C. `2`
D. `4`

Answer

D

Explanation

Difficult: Medium
Category: Passport to Advanced Math/ Exponents
Strategic Advice: You can always rely on the rules of exponents, no matter how strange the exponents may look. Follow the rule for dividing powers of like bases: `(a^(b))/(a^(c))=a^(b-c)`.
Getting to the Answer: Although the left side of the equation seems strange, it melts away once you apply the exponent rule: ltbr. `(a^(x^(2)))/(a^(x^(2)-y^(2)))=a^(x^(2)-(x^(2)-y^(2)))=a^(x^(2)-x^(2)+y^(2))=a^(y^(2))`
So `a^(y^(2))=a^(4)`, which means that `y^(2)=4 and y=2 or, -2.` The question states that `ygt0`, so y must be 2, which is (C).