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Chapter 0: Problem 102

Simplify the expressions. $$ \frac{y^{5 / 4}}{y^{3 / 4}} $$

Short Answer

Expert verified
The simplified expression for \(\frac{y^{5/4}}{y^{3/4}}\) is \(y^{1/2}\).

Step by step solution

01

Identify the rule for dividing expressions with the same base

When dividing expressions with the same base, we can keep the base the same and subtract the exponents. In other words, given the expression \(\frac{a^m}{a^n}\), we can simplify it to \(a^{m-n}\).
02

Apply the rule to the given expression

Now, we need to apply this rule to the given expression, \(\frac{y^{5/4}}{y^{3/4}}\), so we'll keep the base \(y\) and subtract the exponents (5/4) - (3/4).
03

Subtract the exponents

To subtract the exponents, we'll calculate (5/4) - (3/4): \[\frac{5}{4} - \frac{3}{4} = \frac{5 - 3}{4}\]
04

Simplify the result

Now, we can simplify the fraction: \[\frac{2}{4}\] This simplifies to 1/2. So the subtraction of the exponents yields 1/2.
05

Write the final answer

Finally, we can write the simplified expression using the base and the subtracted exponent we calculated: \[y^{1/2}\] So, the simplified expression for \(\frac{y^{5/4}}{y^{3/4}}\) is \(y^{1/2}\).

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Most popular questions from this chapter

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(3\left(1+\frac{4}{100}\right)^{-3}\)

Calculate each expression in Exencises giving the answer as \(a\) whole mumber or a fraction in lowest terms.\(3\left(\frac{1}{9}-\left(\frac{2}{3}\right)^{2}\right)^{2}+1\)

Calculate each expression in Exencises giving the answer as \(a\) whole mumber or a fraction in lowest terms.\(2+4 \cdot 3^{2}\)

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(x^{2}-x+1=0\)

Find all possible real solutions of each equation \(y^{3}+64=0\)
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