Question

6.3 rational exponents quiz

the denominator of a fractional exponent tells you the root.

true
false

Explanation:

Define fractional exponents

A fractional (rational) exponent is an exponent written as a fraction, represented in the general algebraic form:

$$x^{\frac{m}{n}}$$

where \(x\) is the base, and \(m\) and \(n\) are integers with \(n > 0\).

Relate fractional exponents to radicals

By mathematical definition, a fractional exponent can be rewritten in radical form:

$$x^{\frac{m}{n}} = \sqrt[n]{x^m} = (\sqrt[n]{x})^m$$

This definition shows how the numerator and denominator function.

Identify the role of the denominator

In the expression \(\sqrt[n]{x^m}\), the value \(n\) represents the index of the radical, which is commonly referred to as the "root" (for example, a denominator of 2 represents a square root, and 3 represents a cube root). The numerator \(m\) represents the power to which the base is raised.

Evaluate the statement

The given statement is: "The denominator of a fractional exponent tells you the root."
Since the denominator \(n\) in \(x^{\frac{m}{n}}\) corresponds directly to the root index \(\sqrt[n]{\quad}\), this statement is mathematically correct.

Answer:

• True (Correct answer)
• False