Rational Exponents and Radicals
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Lesson Summary:
In this lesson, we learn about rational exponents and how they relate to radicals. We learn that a rational exponent has a meaning in terms of roots and powers, and that the numerator of the rational exponent refers to a power, while the denominator refers to the root. We also learn that perfect squares and perfect cubes are rational numbers, while other radicals are irrational. The lesson concludes with the importance of simplification and rationalizing denominators.
Lesson Description:
An explanation of what rational exponents mean and how they relate to radicals.
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Questions answered by this video:
- What is a rational exponent and how is it the same as a radical?
- How is 4^(1/2) the same as the square root of 4?
- How do you rewrite a rational exponent as a radical expression?
- What is an irrational number?
- How do you simplify 27^(1/3) or the cube root of 27?
- How do you simplify a number raised to a fractional or rational exponent if the numerator is not 1?
- How do you rewrite 4^(4/3) as a radical expression?
- How do you simplify the square root of 16/9?
- How do you simplify the square root of 9*16?
- How do you simplify the cube root of 8*64?
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Staff Review
This lesson explains how a rational or fractional exponent is the same as a radical, how to move back and forth between rational exponents and radical expressions, and how to compute values / simplify these expressions. Many problems are shown and explained in this video.
