Multiple Choice
Use a calculator to evaluate the following and round to the nearest hundredths.
11. Roots, Radicals, and Complex Numbers
Introduction to Radical Expressions
Multiple Choice
Simplify the following.
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Verified step by step guidance1
Start with the expression: \(^4\\sqrt{x^4 y^8}\), which means the fourth root of \(x^4 y^8\).
Recall that the fourth root of a number is the same as raising that number to the power of \(\frac{1}{4}\), so rewrite the expression as \((x^4 y^8)^{\frac{1}{4}}\).
Apply the exponent rule \((a^m)^n = a^{m \cdot n}\) to both \(x^4\) and \(y^8\): this gives \(x^{4 \cdot \frac{1}{4}} y^{8 \cdot \frac{1}{4}}\).
Simplify the exponents by multiplying: \(x^{1} y^{2}\), which is \(x y^2\).
Since we are dealing with even roots, include absolute value signs to ensure the result is non-negative: the simplified form is \(\left| x y^2 \right|\).
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