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$Express the following fraction in simplest form, only using positive exponents. ((3s^(-1))^(3))/(6s^(5)) Answer:$

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{\left(3 s^{-1}\right)^{3}}{6 s^{5}}$ $\newline$ 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{\left(3 s^{-1}\right)^{3}}{6 s^{5}}

\newline

Answer:

Apply Power Rule: Apply the power rule to the numerator. $\newline$ The power rule states that $(a^m)^n = a^{m*n}$ . We will apply this rule to the numerator $(3s^{-1})^3$ . $\newline$ $(3s^{-1})^3 = 3^3 \times (s^{-1})^3$ $\newline$ $= 27 \times s^{-3}$
Rewrite Exponents: Rewrite the expression with positive exponents. $\newline$ To convert negative exponents to positive exponents, we use the rule that $a^{-n} = \frac{1}{a^n}$ . We will apply this to $s^{-3}$ . $\newline$ $27 \times s^{-3} = \frac{27}{s^3}$
Combine Numerator and Denominator: Combine the rewritten numerator with the denominator. $\newline$ Now we have the expression $(27/s^3) / (6s^5)$ . We can simplify this by dividing the coefficients and subtracting the exponents. $\newline$ $(27/s^3) / (6s^5) = 27/(6s^8)$
Simplify Coefficient: Simplify the coefficient. $\newline$ Divide $27$ by $6$ to simplify the coefficient. $\newline$ $\frac{27}{6} = 4.5$ $\newline$ So, the expression becomes $\frac{4.5}{s^8}$ .
Express Coefficient as Fraction: Express the coefficient as a fraction. $\newline$ Since we want the answer in fraction form, we express $4.5$ as a fraction. $\newline$ $4.5 = \frac{9}{2}$ $\newline$ So, the expression becomes $(\frac{9}{2})/s^8$ .
Write Final Answer: Write the final answer. $\newline$ The final answer is the fraction with the positive exponent in the denominator. $\newline$ $(\frac{9}{2})/s^8 = \frac{9}{2s^8}$

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