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If (x^(a^(2)))/(x^(b^(2)))=x^(16), x gt...

If `(x^(a^(2)))/(x^(b^(2)))=x^(16), x gt 1,` and `a+b=2`, what is the value of `a-b`?

A

8

B

14

C

16

D

18

Text Solution

AI Generated Solution

To solve the problem, we start with the given equation: \[ \frac{x^{a^2}}{x^{b^2}} = x^{16} \] Since \(x > 1\), we can use the property of exponents which states that \(\frac{m^a}{m^b} = m^{a-b}\). Therefore, we can rewrite the left-hand side: ...
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