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

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

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Multiplication with rational exponents

Full solution

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

\newline

\frac{2 n^{-2}}{-4(n)^{4}}

\newline

Answer:

Write Expression, Identify Exponents: Write down the given expression and identify negative exponents. $\newline$ The given expression is $(2n^{-2})/(-4(n)^{4})$ . We need to simplify this expression and express it with only positive exponents.
Convert Negative Exponents: Simplify the expression by converting negative exponents to positive exponents. $\newline$ To convert a negative exponent to a positive exponent, we take the reciprocal of the base. So, $n^{-2}$ becomes $1/n^2$ . $\newline$ $(2n^{-2})/(-4(n)^{4}) = (2/(n^2))/(-4n^4)$
Combine Numerator and Denominator: Combine the numerator and denominator. $\newline$ We can combine the terms in the numerator and the denominator by multiplying them. $\newline$ $(2/(n^2))/(-4n^4) = 2/(-4n^6)$
Divide by Greatest Common Factor: Simplify the fraction by dividing both the numerator and the denominator by the greatest common factor. $\newline$ The greatest common factor of $2$ and $-4$ is $2$ . Dividing both the numerator and the denominator by $2$ gives us: $\newline$ $\frac{2}{(-4n^6)} = \frac{(2/2)}{((-4/2)n^6)} = \frac{1}{(-2n^6)}$
Simplify Negative Sign: Simplify the negative sign in the denominator. $\newline$ We can move the negative sign from the denominator to the numerator to make the exponent positive. $\newline$ $\frac{1}{(-2n^6)} = \frac{-1}{2n^6}$

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