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$Express the following fraction in simplest form using only positive exponents. ((4s^(5))^(4))/(2s^(7)) Answer:$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{\left(4 s^{5}\right)^{4}}{2 s^{7}}$ $\newline$ 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{\left(4 s^{5}\right)^{4}}{2 s^{7}}

\newline

Answer:

Apply Power Rule: Apply the power of a power rule to the numerator. $\newline$ The power of a power rule states that $(a^m)^n = a^{m*n}$ . Therefore, we can simplify the numerator as follows: $\newline$ $(4s^{5})^4 = 4^4 \times (s^5)^4$ $\newline$ = $256$ \times s^{ $20$ }
Divide Numerator by Denominator: Divide the numerator by the denominator. $\newline$ Now we have to divide $256 \times s^{20}$ by $2s^{7}$ . When dividing terms with the same base, we subtract the exponents: $\newline$ $\frac{256 \times s^{20}}{2s^{7}} = \frac{256}{2} \times s^{20-7}$ $\newline$ = $128 \times s^{13}$
Check for Simplifications: Check for any remaining simplifications. The expression $128 \times s^{13}$ is already in its simplest form with positive exponents. There are no common factors to reduce, and the exponents are already positive.

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