Simplify the expression.

(3x/x^−5)^0

1 answer

To simplify the expression \((3x/x^{-5})^0\), we need to utilize the property of exponents that states any non-zero base raised to the power of \(0\) is equal to \(1\).

First, we check the base of the expression:

\[ \frac{3x}{x^{-5}} = 3x \cdot x^5 = 3x^{1 + 5} = 3x^6 \]

Now, observe the entire expression:

\[ (3x/x^{-5})^0 = (3x^6)^0 \]

Since \(3x^6\) is not zero (assuming \(x \neq 0\)), we apply the exponent rule:

\[ (3x^6)^0 = 1 \]

Thus, the simplified expression is:

\[ \boxed{1} \]