How to Simplify Expressions with Rational Exponents and Radicals?

What is a rational exponent?

A. An exponent that can be expressed as a fraction

B. An exponent that is a whole number

C. An exponent that is irrational

Answer:

The correct answer is A. An exponent that can be expressed as a fraction.

When simplifying expressions with rational exponents and radicals, it is important to understand what rational exponents are. Rational exponents can be expressed as fractions, meaning the exponent is not a whole number or irrational number. By using rational exponents, we can simplify expressions involving radicals and exponents more easily.

For example, in the expression ∛(x^4), the rational exponent is 4/3 because the cube root (∛) of x^4 can be written as x^(4/3). This allows us to simplify the expression and perform calculations more efficiently.

By mastering the concept of rational exponents, you can simplify complex expressions and solve mathematical problems with ease.