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Chapter 7: Problem 58

Simplify each number. $$64^{-0.5}$$

Short Answer

Expert verified
The simplified form of \(64^{-0.5}\) is \(\frac{1}{8}\)

Step by step solution

01

Understanding Negative Exponents

In the given expression, the exponent is negative. A negative exponent means we take the reciprocal (1 divided by the number) of the base. So, we rewrite \(64^{-0.5}\) as \(\frac{1}{64^{0.5}}\).
02

Understanding fractional Exponents

The number 0.5 as an exponent is equivalent to taking the square root of the base. Therefore, we simplify \(\frac{1}{64^{0.5}}\) as \(\frac{1}{\sqrt{64}}\).
03

Calculating the Square Root

The square root of 64 equals 8. Therefore, the expression simplifies to \(\frac{1}{8}\).

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