Simplify the expression. (10m^(6)n^(3))/(5m^(2)n^(7))

Simplify Coefficients: Simplify the coefficients. Divide the coefficients 10 by 5. 10 / 5 = 2Apply Quotient Rule for m: Apply the quotient rule for exponents to m. The quotient rule states that when dividing like bases, you subtract the exponents. m^(6) / m^(2) = m^(6-2) = m^(4)Apply Quotient Rule for n: Apply the quotient rule for exponents to n. The quotient rule states that when dividing like bases, you subtract the exponents. n^(3) / n^(7) = n^(3-7) = n^(-4)Combine Results: Combine the results from Steps 1, 2, and 3. 2 * m^(4) * n^(-4)Write Final Expression: Write the final simplified expression. Since n^(-4) is the same as 1/n^(4), we can rewrite the expression as: 2m^(4)/n^(4)

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Calculus

Find derivatives of using multiple formulae

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Q. Simplify the expression.

\newline

\frac{10 m^{6} n^{3}}{5 m^{2} n^{7}}

Simplify Coefficients: Simplify the coefficients. $\newline$ Divide the coefficients $10$ by $5$ . $\newline$ $10 / 5 = 2$
Apply Quotient Rule for $m$ : Apply the quotient rule for exponents to $m$ . The quotient rule states that when dividing like bases, you subtract the exponents. $m^{6} / m^{2} = m^{6-2} = m^{4}$
Apply Quotient Rule for $n$ : Apply the quotient rule for exponents to $n$ . The quotient rule states that when dividing like bases, you subtract the exponents. $\frac{n^{3}}{n^{7}} = n^{3-7} = n^{-4}$
Combine Results: Combine the results from Steps $1$ , $2$ , and $3$ . $2 \times m^{4} \times n^{-4}$
Write Final Expression: Write the final simplified expression. $\newline$ Since $n^{-4}$ is the same as $1/n^{4}$ , we can rewrite the expression as: $\newline$ $2m^{4}/n^{4}$