Simplify using properties of exponents. 20 x 1 2 5 x 1 4 \frac{20x^{\frac{1}{2}}}{5x^{\frac{1}{4}}} 5 x 4 1 20 x 2 1

Welcome back. I'm so glad you're here. We are simplifying this expression, we've got two terms that are being multiplied. We can start off with the coefficients. We've got six times three. Yeah, that's 18. And yeah, our answer choices are 18. So yeah, we did that right. And now we've got the tricky part, we've got the white of the 4/5 and we've got the y to the nine over to the nine seconds and we've got two exponents that are being multiplied. We are going to add them together. So what we're going to add 4/5 plus nine seconds. And in order to add two fractions, we've got to have a common denominator. Common denominator between five and two is 10. We look at each of those and we say how do we get from 5 to 10? We've got to multiply it by two. Do the same to the top and the bottom. So in effect we're multiplying it by one, we look at to how do we get from 2 to 10? We multiply by five. What we do to the bottom. We've got to do that. The top. So that in effect we're multiplying it by one. We'll go ahead and do that multiplication and we'll get 8/10 plus 45/10, combining those enumerators, we get 53 the denominator stays and that is as simplified as that one is going to get. So we've got 18 Y to the 53/10. That's as simplified as we can do. We look at the answer choices and that is answer choice. A well done, we'll catch you on the next one.

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

1:31 minutes

Problem 93

Textbook Question

Simplify using properties of exponents. $\frac{20x^{\frac{1}{2}}}{5x^{\frac{1}{4}}}$

Verified step by step guidance

Identify the expression to simplify: $\frac{20x^{\frac{1}{2}}}{5x^{\frac{1}{4}}}$.

Simplify the coefficients (numerical parts) by dividing 20 by 5: $\frac{20}{5} = 4$.

Apply the quotient rule for exponents to the variable part: $\frac{x^{\frac{1}{2}}}{x^{\frac{1}{4}}} = x^{\frac{1}{2} - \frac{1}{4}}$.

Subtract the exponents: $\frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}$, so the variable part becomes $x^{\frac{1}{4}}$.

Combine the simplified coefficient and variable parts to write the simplified expression: \$4x^{\frac{1}{4}}$.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Properties of Exponents

Properties of exponents are rules that simplify expressions involving powers of the same base. Key properties include the quotient rule, which states that when dividing like bases, subtract the exponents (a^m / a^n = a^(m-n)). These rules help in simplifying expressions with fractional exponents.

Fractional Exponents

Fractional exponents represent roots and powers simultaneously. For example, x^(1/2) means the square root of x, and x^(1/4) means the fourth root of x. Understanding how to manipulate fractional exponents is essential for simplifying expressions involving roots.

Simplifying Rational Expressions

Simplifying rational expressions involves reducing fractions by factoring and canceling common terms. When variables with exponents appear in numerator and denominator, apply exponent rules to combine or reduce terms, making the expression simpler and easier to interpret.

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