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$Express the following fraction in simplest form using only positive exponents. (12t^(8))/(4(t^(2))^(3)) Answer:$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{12 t^{8}}{4\left(t^{2}\right)^{3}}$ $\newline$ Answer:

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Simplify variable expressions using properties

Full solution

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

\newline

\frac{12 t^{8}}{4\left(t^{2}\right)^{3}}

\newline

Answer:

Simplify Fraction: Simplify the fraction by dividing the numerator and the denominator by their greatest common factor. $\newline$ The greatest common factor of $12$ and $4$ is $4$ . Divide both the numerator and the denominator by $4$ . $\newline$ $\frac{12t^{8}}{4(t^{2})^{3}} = \frac{12}{4}t^{8}/(t^{2})^{3}$ $\newline$ = $3t^{8}/t^{6}$
Divide by Common Factor: Simplify the expression by using the laws of exponents. $\newline$ When dividing like bases, subtract the exponents. $\newline$ $3t^{8}/(t^{6}) = 3t^{8-6}$ $\newline$ $= 3t^{2}$

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