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Exercises 2.5 Exercises
1. Evaluating Negative and Rational Exponents.
Find the exact value of each expression without using a calculator.
\(\displaystyle 2^{-4}\)
\(\displaystyle 4^{-1/2}\)
\(\displaystyle -8^{4/3}\)
\(\displaystyle (-8)^{4/3}\)
\(\displaystyle 8^{-4/3}\)
\(\displaystyle -8^{-4/3}\)
Answer.
\(\displaystyle 2^{-4} = 1/16\)
\(\displaystyle 4^{-1/2} = 1/2\)
\(\displaystyle -8^{4/3} = -16\)
\(\displaystyle (-8)^{4/3} = 16\)
\(\displaystyle 8^{-4/3} = 1/16\)
\(\displaystyle -8^{-4/3} = -1/16\)
2. Using Laws of Exponents.
Find the exact value \(\left(\frac{2^0-2^1}{2^2}\right)^{-3}\) without using a calculator.
