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Answer
The simplified form is \( -\frac{8}{x^{6}y^{9}} \).
Solution
Calculate or simplify the expression \( (-2*x^(-2)*y^(-3))^3 \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(-2x^{-2}y^{-3}\right)^{3}\)
- step1: Determine the sign:
\(-\left(2x^{-2}y^{-3}\right)^{3}\)
- step2: Use the properties of exponents:
\(-2^{3}\left(x^{-2}\right)^{3}\left(y^{-3}\right)^{3}\)
- step3: Evaluate the power:
\(-8x^{-6}y^{-9}\)
- step4: Simplify:
\(-\frac{8}{x^{6}y^{9}}\)
The simplified form of \( \left(-2 x^{-2} y^{-3}\right)^{3} \) is \( -\frac{8}{x^{6}y^{9}} \).
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Simplify this solution The Deep Dive
To simplify the expression \( \left(-2 x^{-2} y^{-3}\right)^{3} \), you need to apply the power of a product rule, which states that you raise each component inside the parentheses to the power outside. This gives you: \[ (-2)^3 \cdot (x^{-2})^3 \cdot (y^{-3})^3 = -8 \cdot x^{-6} \cdot y^{-9} \] Now, to express it in a more standard form, you can rewrite the expression using positive exponents: \[ -\frac{8}{x^{6} y^{9}} \] And there you have it! The simplified form is: \[ -\frac{8}{x^{6} y^{9}} \]
