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MODULE 3: RATIONAL EXPONENTS AND SIMPLIFYING RADICALS New York City College of Technology MAT 1275 PAL Workshops Name: 1. Points: Rational Exponents a. The expression a b. The expression a1 n m NIN

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How to fill out rational exponents and simplifying

01

To fill out rational exponents and simplify, follow these steps: 1. Start by determining the base and exponent of the rational exponent. For example, in the expression (4/5)^(3/2), the base is 4/5 and the exponent is 3/2.

02

Convert the rational exponent to a fractional exponent. To do this, rewrite the exponent as a fraction with a numerator and a denominator. For example, the exponent 3/2 can be written as 3^(1/2).

03

Apply the fractional exponent to the base using the power rule. Raise the base to the numerator of the fractional exponent and take the root of the result with the denominator. For example, (4/5)^(3/2) can be simplified to (4/5)^(3^(1/2)) = √(4/5)^3.

04

Simplify the expression further if possible. In this case, you can simplify (√(4/5)^3) by evaluating the square root and raising the result to the power of 3. The final simplified form would be (√(4/5))^3 = (2/√5)^3 = (2^3)/(√5^3) = 8/(√5^3).

Who needs rational exponents and simplifying?

01

Rational exponents and simplifying are essential concepts in algebra and higher-level mathematics. They are primarily needed by students studying advanced math subjects, such as calculus, linear algebra, and discrete mathematics.

02

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03

In general, anyone who wants to have a solid understanding of algebraic manipulations and solve equations involving fractional exponents will benefit from learning how to work with rational exponents and simplifying.

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