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\( 4^{-3} = \frac{1}{64} \)
Solución
To evaluate \( 4^{-3} \), we can use the property of negative exponents, which states:
\[
a^{-n} = \frac{1}{a^n}
\]
Applying this property to \( 4^{-3} \):
\[
4^{-3} = \frac{1}{4^3}
\]
Now, calculate \( 4^3 \):
\[
4^3 = 4 \times 4 \times 4 = 64
\]
So,
\[
4^{-3} = \frac{1}{64}
\]
**Final Answer:**
\[
4^{-3} = \frac{1}{64}
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Mind Expander
Did you know that \( 4^{-3} \) is an example of using negative exponents? Negative exponents indicate the reciprocal of the positive exponent. So, \( 4^{-3} \) can be rewritten as \( \frac{1}{4^3} \), which equals \( \frac{1}{64} \). It’s a neat trick that makes calculations easier! Now, let's consider the real-world application of this concept. Understanding negative exponents is crucial in fields like engineering and computer science, where exponential decay and growth are common. For instance, in electronics, the concept can apply to the decay of electrical signals, helping engineers predict how quickly a signal will diminish over distances—pretty cool, right?
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