Question
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form is \( \frac{1}{x} \).
Solution
Calculate or simplify the expression \( (2*x^(-2))^(-1) * 2*x^(-3) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(2x^{-2}\right)^{-1}\times 2x^{-3}\)
- step1: Multiply the terms:
\(x^{2}\times x^{-3}\)
- step2: Simplify the expression:
\(x^{2-3}\)
- step3: Subtract the numbers:
\(x^{-1}\)
- step4: Simplify:
\(\frac{1}{x}\)
The simplified form of \( \left(2 x^{-2}\right)^{-1} \cdot 2 x^{-3} \) is \( \frac{1}{x} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
First, let's simplify the expression \( \left(2 x^{-2}\right)^{-1} \). When you take the reciprocal of a term, you flip it over which gives us \( \frac{1}{2 x^{-2}} = \frac{x^{2}}{2} \). Now, substituting back into the expression, we have: \[ \frac{x^{2}}{2} \cdot 2 x^{-3} \] This simplifies to: \[ \frac{2 x^{2} \cdot x^{-3}}{2} \] The '2' cancels out, leaving us with: \[ x^{2} \cdot x^{-3} = x^{2 - 3} = x^{-1} \] So, the final answer is: \[ x^{-1} \] or \(\frac{1}{x}\) if you prefer to express it in a positive exponent form.
