Pregunta
Rewrite the following without an exponent. \[ 4^{-3} \]
Ask by Wang Griffin. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\( 4^{-3} \) can be written as \( \frac{1}{4 \times 4 \times 4} \).
Solución
Certainly! The expression \( 4^{-3} \) can be rewritten without using an exponent by expressing it as a reciprocal multiplied by itself three times. Here is the rewritten form:
\[
\frac{1}{4 \times 4 \times 4}
\]
**Explanation:**
- A negative exponent indicates that the base is on the wrong side of a fraction. Specifically, \( 4^{-3} \) means the reciprocal of \( 4^3 \).
- Instead of using an exponent, multiply the base (4) by itself three times in the denominator.
So, \( 4^{-3} \) is equivalent to \( \frac{1}{4 \times 4 \times 4} \).
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Mind Expander
To rewrite \( 4^{-3} \) without an exponent, you can use the rule that states a negative exponent indicates a reciprocal. Thus, \( 4^{-3} \) can be expressed as: \[ \frac{1}{4^3} \] Next, calculate \( 4^3 \): \[ 4^3 = 4 \times 4 \times 4 = 64 \] Therefore, \( 4^{-3} \) can be rewritten as: \[ \frac{1}{64} \]
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