Question

rewrite the expression in the form $k \cdot y^n$.
write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
$\frac{8y^2}{2\sqrt4{y}} = $

Explanation:

Step1: Simplify the coefficient

First, simplify the coefficient part. We have \(\frac{8}{2}\), which equals \(4\).

Step2: Simplify the variable part

Next, handle the variable part. Recall that \(\sqrt[4]{y}=y^{\frac{1}{4}}\), so the denominator \(2\sqrt[4]{y}\) has the variable part \(y^{\frac{1}{4}}\). When dividing exponents with the same base, we subtract the exponents: \(y^{2}\div y^{\frac{1}{4}} = y^{2-\frac{1}{4}}\). Calculate \(2-\frac{1}{4}=\frac{8}{4}-\frac{1}{4}=\frac{7}{4}\).

Step3: Combine coefficient and variable

Now, combine the simplified coefficient and the simplified variable part. The coefficient is \(4\) and the variable part is \(y^{\frac{7}{4}}\), so the expression becomes \(4\cdot y^{\frac{7}{4}}\).

Answer:

\(4\cdot y^{\frac{7}{4}}\)