Pregunta
Evaluate the numerical expression. \[ (-64)^{1 / 3} \]
Ask by Rodriquez Evans. in the United States
Mar 21,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\[
(-64)^{\frac{1}{3}} = -4
\]
Solución
We start by recognizing that exponentiation with a fractional exponent represents a root. In this case, the exponent \( \frac{1}{3} \) represents the cube root. That is,
\[
(-64)^{\frac{1}{3}} = \sqrt[3]{-64}.
\]
Since the cube root of a negative number is negative, we can write:
\[
\sqrt[3]{-64} = -\sqrt[3]{64}.
\]
Now, note that \( 64 = 4^3 \). Therefore,
\[
\sqrt[3]{64} = 4.
\]
Putting it all together:
\[
(-64)^{\frac{1}{3}} = -4.
\]
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Simplifique esta solución Mind Expander
The expression \( (-64)^{1 / 3} \) refers to the cube root of \(-64\). To find the cube root, you need to determine which number, when multiplied by itself three times, equals \(-64\). The answer is \(-4\), since \(-4 \times -4 \times -4 = -64\). Therefore, the result of the expression is: \[ (-64)^{1 / 3} = -4 \]
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