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Here are a few recommended readings before getting started with this lesson.
Here are a few practice exercises before getting started with this lesson.
Calculate the value of the following expressions. Write the answer as an integer number or as a fraction in its simplest form.
The exponent of an expression indicates how many times the base is multiplied by itself.
Power | Multiplication | Value |
---|---|---|
42 | 4⋅4 | 16 |
23 | 2⋅2⋅2 | 8 |
54 | 5⋅5⋅5⋅5 | 625 |
15 | 1⋅1⋅1⋅1⋅1 | 1 |
The relationship between rational exponents and roots can be extended to any rational exponent of the form n1, where n is a natural number.
Dominika pays 62541 dollars per hour to study with a private tutor.
As her first homework assignment, she was given the task of writing how much she pays per hour as a radical. Write her answer without including the currency symbol.
Calculate the values of the given powers with rational exponents by using a radical.
Consider a right triangle in which the legs are two sides of the square and the hypotenuse is the diagonal.
Consider the right triangle formed by two sides of the square and its diagonal.
Here, the length of both legs is 1. Therefore, by substituting a=1 and b=1 into the Pythagorean Theorem, the length of the diagonal c can be found.a=1, b=1
1a=1
Add terms
LHS=RHS
a2=a
Rearrange equation
Note that the numerator of a rational number does not have to be 1, but could also be any integer number. Therefore, rational numbers with a numerator different than 1 should also be considered as rational exponents.
Ignacio ate some cake at a birthday party. When he arrived home, he told his parents that he had 832 slices.
His mother, who is a math teacher, asked him to express the number of slices that he ate as a radical.Start by writing both numeric expressions using radicals.