Problem 58 - Algebra 2

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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 \(\frac{1}{64^{0.5}}\).

Step 2: 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 \(\frac{1}{\sqrt{64}}\).

Step 3: Calculating the Square Root

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