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$Express the following fraction in simplest form, only using positive exponents. ((-4y^(4))^(2))/(-5y^(3)) Answer:$

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{\left(-4 y^{4}\right)^{2}}{-5 y^{3}}$ $\newline$ Answer:

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

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

\newline

\frac{\left(-4 y^{4}\right)^{2}}{-5 y^{3}}

\newline

Answer:

Identify Base and Exponents: Write down the given expression and identify the base and exponents. $\newline$ The given expression is $((-4y^{4})^{2})/(-5y^{3})$ . $\newline$ Here, we have a power to a power for the numerator, which means we will multiply the exponents, and a negative base for the denominator.
Apply Power to Power Rule: Apply the power to a power rule to the numerator. $\newline$ $((-4y^{4})^{2}) = (-4)^{2} \times (y^{4})^{2}$ $\newline$ According to the power to a power rule, $(a^{m})^{n} = a^{m\times n}$ . $\newline$ So, we have $(-4)^{2} \times y^{4\times 2} = 16 \times y^{8}$ .
Simplify Denominator: Simplify the denominator. $\newline$ The denominator is $-5y^{3}$ . Since we want only positive exponents, we leave the denominator as it is because the exponent on $y$ is already positive.
Combine Numerator and Denominator: Combine the simplified numerator and denominator. $\newline$ Now we have $16 \times y^{8}$ for the numerator and $-5y^{3}$ for the denominator. $\newline$ So, the expression becomes $(16 \times y^{8}) / (-5y^{3})$ .
Divide Coefficients and Subtract Exponents: Divide the coefficients and subtract the exponents of like bases. $\newline$ Divide $16$ by $-5$ to get $-\frac{16}{5}$ . $\newline$ Subtract the exponents of $y$ : $y^{(8-3)} = y^{5}$ . $\newline$ The expression now is $(-\frac{16}{5})y^{5}$ .
Write Final Simplified Expression: Write the final simplified expression. $\newline$ The final simplified expression is $\frac{-16}{5}y^{5}$ .