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Chapter 8: Problem 46

Rewrite the radical expression in exponential notation. $$\sqrt[4]{y^{3}}$$

Short Answer

Expert verified
y^{\frac{3}{4}}

Step by step solution

01

Understand the radical notation

Identify the parts of the radical expression. In this case, \(\text{鈭歔4]{y^{3}}} \), the '4' is the index of the root, and \(\text{y^{3}}\) is the radicand.
02

Rewrite using fractional exponents

Recall that a radical expression can be rewritten in exponential notation by using fractional exponents. The general form is \(\text{鈭歔n]{a^{m}}} = a^{\frac{m}{n}}\).
03

Apply the rule

Applying this rule to our specific problem: \(\text{鈭歔4]{y^{3}} = y^{\frac{3}{4}}}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

radical expression
A radical expression involves the concept of a root. It is represented by the symbol called the radical sign (鈭�).
The expression inside the radical sign is the radicand.
For example, in the expression \(\sqrt[4]{y^{3}}\), we have a radical expression: \(\sqrt{....}\).
Radical expressions are used to represent roots of numbers or variables.
fractional exponents
Fractional exponents are another way to represent roots.
Instead of writing a root symbol (鈭�), we can use an exponent that is a fraction.
The numerator of the fraction is the power of the radicand, and the denominator is the index of the root.
For example, \(\sqrt[4]{y^{3}}\) can also be written as \(y^{\frac{3}{4}}\).
This method simplifies many algebraic operations.
index of the root
The index of the root is the small number written just outside and above the radical sign.
It indicates the degree of the root being taken.
In \(\sqrt[4]{y^{3}}\), the index is '4', meaning the fourth root.
If there is no number, it defaults to 2, indicating a square root.
Changing the index affects the value of the root.
radicand
The radicand is the value inside the radical sign.
It is the quantity from which we want to take the root.
In \(\sqrt[4]{y^{3}}\), the radicand is \(y^{3}\).
The radicand can be a number, variable, or more complex expression.
Understanding the radicand helps in converting to exponential notation and performing algebraic operations more easily.

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Most popular questions from this chapter

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