To solve the equation \(\frac{x^{5/3}}{x^{6/5}} = x^a\), we can use the property of exponents \(\frac{x^m}{x^n} = x^{m-n}\).
Now, we can rewrite the left-hand side:
\[ \frac{x^{5/3}}{x^{6/5}} = x^{5/3 - 6/5} \]
Next, we need to compute \(5/3 - 6/5\). To perform this subtraction, we need a common denominator. The least common multiple of 3 and 5 is 15. So we will convert each fraction:
\[ 5/3 = \frac{5 \cdot 5}{3 \cdot 5} = \frac{25}{15} \]
\[ 6/5 = \frac{6 \cdot 3}{5 \cdot 3} = \frac{18}{15} \]
Now we can subtract:
\[ \frac{25}{15} - \frac{18}{15} = \frac{25 - 18}{15} = \frac{7}{15} \]
So, we have:
\[ \frac{x^{5/3}}{x^{6/5}} = x^{\frac{7}{15}} \]
Therefore, the equation simplifies to:
\[ x^{\frac{7}{15}} = x^a \]
This implies that:
\[ a = \frac{7}{15} \]
Thus, the value of \(a\) is \(\frac{7}{15}\).
So the correct answer is:
\(a = 7/15\)
A is equal to 7 over 15.
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