Asked by hola
Simplify the expression.
(3x/x^−5)^0
(3x/x^−5)^0
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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:
\[
\boxed{1}
\]
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:
\[
\boxed{1}
\]
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