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La expresión simplificada es \( -\frac{g^{12}}{27h^{9}} \).
Solución
Calculate or simplify the expression \( (-3*g^{-4}*h^{3})^{-3} \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(-3g^{-4}h^{3}\right)^{-3}\)
- step1: Determine the sign:
\(-\left(3g^{-4}h^{3}\right)^{-3}\)
- step2: Use the properties of exponents:
\(-3^{-3}\left(g^{-4}\right)^{-3}\left(h^{3}\right)^{-3}\)
- step3: Evaluate the power:
\(-\frac{1}{27}g^{12}h^{-9}\)
- step4: Simplify:
\(-\frac{g^{12}}{27h^{9}}\)
La expresión \( \left(-3 g^{-4} h^{3}\right)^{-3} \) se simplifica a \( -\frac{g^{12}}{27h^{9}} \).
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Simplifique esta solución Mind Expander
To simplify the expression \( \left(-3 g^{-4} h^{3}\right)^{-3} \), we first need to apply the power of a product rule. This means raising each factor inside the parentheses to the power of \(-3\). 1. The constant \(-3\) raised to the power of \(-3\) is \(-\frac{1}{27}\). 2. For \(g^{-4}\), applying the exponent we get \(g^{-4 \times -3} = g^{12}\). 3. For \(h^{3}\), we similarly find \(h^{3 \times -3} = h^{-9}\), which can also be expressed as \(\frac{1}{h^{9}}\). So, putting it all together, we have: \[ \left(-3 g^{-4} h^{3}\right)^{-3} = -\frac{1}{27} g^{12} h^{-9} = -\frac{g^{12}}{27 h^{9}} \] Thus, the simplified expression is \( -\frac{g^{12}}{27 h^{9}} \).
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