Solve (x - 4)^(2/3) = 36 College Algebra MyMathlab Homework | Summary and Q&A

TL;DR

Learn how to solve equations with rational exponents by eliminating the denominator and using the square root property.

Key Insights

• ✊ Solving equations with rational exponents involves eliminating the denominator by raising both sides to a power that cancels out the denominator.
• ❎ The square root property is used when an equation has a variable squared and set equal to a constant.
• 😑 Simplifying expressions with rational exponents requires applying the properties of exponents, such as multiplying the numerator and denominator by the reciprocal to eliminate the rational exponent.

Transcript

and this problem we have an equation with rational exponents so we have X minus 4 to the 2/3 power that's equal to 36 so when you have an equation with rational exponents you want to focus on getting rid of the bottom of bottom number first so we'll start by rewriting it X minus 4 to the 2/3 equals 36 and then we'll just cube both sides that will g... Read More

Questions & Answers

Q: How do you solve an equation with rational exponents?

To solve an equation with rational exponents, start by eliminating the denominator by raising both sides of the equation to the power of the reciprocal of the exponent. This allows you to work with integer exponents and solve for the variable.

Q: What is the square root property?

The square root property states that if a^2 = b, then a = sqrt(b) or a = -sqrt(b). This property is used when you have an equation where the variable is squared and set equal to a constant.

Q: Why do we cube both sides of the equation?

When solving an equation with rational exponents, cubing both sides allows us to eliminate the denominator. This is because cubing a rational exponent gives us an equivalent equation with an integer exponent.

Q: How do you simplify expressions with rational exponents?

To simplify expressions with rational exponents, apply the properties of exponents. For example, X^(7/8) can be simplified by raising both sides of the equation to the power of the reciprocal of the exponent - in this case, the 8th power.

Summary & Key Takeaways

• The video explains how to solve an equation with rational exponents, using the example of (X - 4)^(2/3) = 36.

• To eliminate the denominator, cube both sides of the equation, resulting in (X - 4)^2 = 36^3.

• Next, apply the square root property to find the value of X, resulting in two possible solutions: X = 220 and X = 212.