Multiple Choice
Use a calculator to evaluate the following and round to the nearest hundredths.
9. Roots, Radicals, and Complex Numbers
Introduction to Radical Expressions
Multiple Choice
Simplify the following.
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Verified step by step guidance1
Recognize that the expression involves the fourth root of a product: \(^4\sqrt{x^4 y^8}\). The fourth root means raising the inside expression to the power of \(\frac{1}{4}\).
Rewrite the expression using fractional exponents: \(\left(x^4 y^8\right)^{\frac{1}{4}}\).
Apply the power of a product rule: \(\left(x^4\right)^{\frac{1}{4}} \cdot \left(y^8\right)^{\frac{1}{4}}\).
Simplify each term by multiplying the exponents: \(x^{4 \cdot \frac{1}{4}} \cdot y^{8 \cdot \frac{1}{4}}\), which simplifies to \(x^1 \cdot y^2\) or \(x y^2\).
Since the original expression involves an even root (fourth root), include absolute value signs to ensure the result is nonnegative: \(\left| x y^2 \right|\).
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