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$Express the following fraction in simplest form using only positive exponents. (2(d^(4))^(3))/(6d^(5)) Answer:$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{2\left(d^{4}\right)^{3}}{6 d^{5}}$ $\newline$ 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{2\left(d^{4}\right)^{3}}{6 d^{5}}

\newline

Answer:

Simplify numerator: Simplify the numerator. $\newline$ The numerator is $2(d^{4})^{3}$ . According to the power of a power rule, $(a^{m})^{n} = a^{m*n}$ , we multiply the exponents. $\newline$ $2(d^{4*3})$ $\newline$ = $2(d^{12})$
Simplify denominator: Simplify the denominator. $\newline$ The denominator is $6d^{5}$ . There is nothing to simplify here, so we keep it as is. $\newline$ $6d^{5}$
Divide numerator by denominator: Divide the numerator by the denominator. $\newline$ Now we divide the terms in the numerator by the corresponding terms in the denominator. $\newline$ $(2d^{12})/(6d^{5})$ $\newline$ We can divide the coefficients $(2/6)$ and subtract the exponents of $d$ $(d^{12-5})$ since the bases are the same. $\newline$ $(1/3)d^{12-5}$ $\newline$ = $(1/3)d^{7}$
Check for further simplification: Check for any further simplification. $\newline$ The fraction $(\frac{1}{3})d^{7}$ is already in its simplest form with positive exponents. There are no common factors to cancel out, and the exponent is already positive.

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