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$Rewrite the expression in the form k*y^(n). Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). (8y^(2))/(2root(4)(y))=◻$

Rewrite the expression in the form $k \cdot y^{n}$ . $\newline$ Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). $\newline$ $\frac{8 y^{2}}{2 \sqrt[4]{y}}=\square$

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Evaluate variable expressions involving rational numbers

Full solution

Q. Rewrite the expression in the form

k \cdot y^{n}

.

\newline

Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).

\newline

\frac{8 y^{2}}{2 \sqrt[4]{y}}=\square

Simplify Coefficients and Root: We are given the expression $(8y^{2})/(2\sqrt[4]{y})$ . The first step is to simplify the expression by dividing the coefficients and rewriting the root as an exponent. $\newline$ Divide $8$ by $2$ . $\newline$ $8 / 2 = 4$ $\newline$ Rewrite the fourth root of y as $y^{1/4}$ . $\newline$ Expression becomes: $4y^{2} \cdot y^{-1/4}$
Combine Like Terms: Now we need to combine the $y$ terms by adding their exponents, since they have the same base and are being multiplied. $\newline$ Use the rule: $y^{a} \cdot y^{b} = y^{a+b}$ $\newline$ Add the exponents $2$ and $-\frac{1}{4}$ . $\newline$ $2 + (-\frac{1}{4}) = 2 - \frac{1}{4} = \frac{8}{4} - \frac{1}{4} = \frac{7}{4}$ $\newline$ Expression becomes: $4y^{\frac{7}{4}}$

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