Multiple Choice
Evaluate the following square root.
9. Roots, Radicals, and Complex Numbers
Introduction to Radical Expressions
Multiple Choice
Simplify the root.
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Verified step by step guidance1
Identify the expression to simplify: the fourth root of the square root of 256, which can be written as \(\sqrt[4]{\sqrt{256}}\).
Rewrite the nested roots using fractional exponents: the square root of 256 is \(256^{\frac{1}{2}}\), so the expression becomes \(\left(256^{\frac{1}{2}}\right)^{\frac{1}{4}}\).
Apply the power of a power rule by multiplying the exponents: \(256^{\frac{1}{2} \times \frac{1}{4}} = 256^{\frac{1}{8}}\).
Express 256 as a power of 2 to simplify the exponent: since \$256 = 2^8$, substitute to get \(\left(2^8\right)^{\frac{1}{8}}\).
Again, apply the power of a power rule by multiplying exponents: \(2^{8 \times \frac{1}{8}} = 2^1\), which simplifies the expression.
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