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

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

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Multiplication with rational exponents

Full solution

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

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\frac{5 c^{6}}{\left(4 c^{3}\right)^{4}}

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Answer:

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Submit Answer

Simplify Denominator: Simplify the denominator. $\newline$ The denominator is $(4c^{3})^{4}$ . According to the power of a power rule, we multiply the exponents. $\newline$ $(4c^{3})^{4} = 4^{4} \times (c^{3})^{4}$ $\newline$ Now, calculate the powers. $\newline$ $4^{4} = 4 \times 4 \times 4 \times 4 = 256$ $\newline$ $(c^{3})^{4} = c^{3\times4} = c^{12}$ $\newline$ So, the denominator becomes $256c^{12}$ .
Write Simplified Fraction: Write the simplified fraction. $\newline$ Now we have the numerator as $5c^{6}$ and the denominator as $256c^{12}$ . $\newline$ The fraction is: $\newline$ $\frac{5c^{6}}{256c^{12}}$
Cancel Common Factors: Simplify the fraction by canceling common factors. $\newline$ We can divide both the numerator and the denominator by $c^{6}$ since it is the highest power of $c$ that divides both terms. $\newline$ $(5c^{6}) / (256c^{12}) = (5/c^{6}) / (256/c^{12})$ $\newline$ Now, subtract the exponents of $c$ in the numerator and denominator. $\newline$ $c^{6} / c^{12} = c^{6-12} = c^{-6}$ $\newline$ So, the fraction simplifies to: $\newline$ $5 / (256c^{-6})$
Express Fraction with Positive Exponents: Express the fraction using only positive exponents. $\newline$ To express $c^{-6}$ with a positive exponent, we take the reciprocal of $c^{6}$ . $\newline$ $\frac{5}{256c^{-6}} = \frac{5}{256 / c^{6}} = \frac{5c^{6}}{256}$

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