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$Express the following fraction in simplest form using only positive exponents. ((2y^(4))^(2))/(4y) Answer:$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{\left(2 y^{4}\right)^{2}}{4 y}$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

Q. Express the following fraction in simplest form using only positive exponents.

\newline

\frac{\left(2 y^{4}\right)^{2}}{4 y}

\newline

Answer:

Identify Given Expression: Write down the given expression and identify the properties of exponents that can be applied. $\newline$ The given expression is $\frac{(2y^{4})^{2}}{4y}$ . We can apply the power of a power property for the numerator and the quotient of powers property for the denominator.
Apply Power of Power: Apply the power of a power property to the numerator. $\newline$ $(2y^{4})^{2} = 2^{2} \times (y^{4})^{2}$ $\newline$ Using the power of a power property, we multiply the exponents for $y$ . $\newline$ $= 4 \times y^{4\times2}$ $\newline$ $= 4 \times y^{8}$
Simplify Denominator: Simplify the denominator. $\newline$ The denominator is $4y$ , which can be written as $4 \times y^{1}$ to make the exponents explicit.
Divide Numerator by Denominator: Divide the numerator by the denominator. $\newline$ Now we divide $4 \cdot y^{8}$ by $4 \cdot y^{1}$ . $\newline$ $(4 \cdot y^{8}) / (4 \cdot y^{1}) = (4/4) \cdot (y^{8}/y^{1})$
Simplify Fraction: Simplify the fraction. $\newline$ $\frac{4}{4}$ simplifies to $1$ , and using the quotient of powers property, we subtract the exponents for $y$ . $\newline$ $1 \times y^{8-1} = y^{7}$
Write Final Expression: Write the final simplified expression. $\newline$ The expression in simplest form using only positive exponents is $y^{7}$ .

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