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$Express the following fraction in simplest form using only positive exponents. (2m^(9))/((4m^(5))^(4)) Answer: Submit Answer$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{2 m^{9}}{\left(4 m^{5}\right)^{4}}$ $\newline$ 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{2 m^{9}}{\left(4 m^{5}\right)^{4}}

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Answer:

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Submit Answer

Identify Base and Exponents: Write down the given expression and identify the base and exponents. $\newline$ We have the expression $(2m^{9})/((4m^{5})^{4})$ . $\newline$ Here, we need to simplify the expression by dealing with the exponents and the base.
Apply Power of Power Rule: Apply the power of a power rule to the denominator. $\newline$ The power of a power rule states that $(a^b)^c = a^{(b*c)}$ . $\newline$ So, $(4m^{5})^{4}$ becomes $4^{4} \times m^{(5*4)}$ which is $4^{4} \times m^{20}$ .
Calculate Denominator Value: Calculate the value of $4^{4}$ . $4^{4}$ is $4 \times 4 \times 4 \times 4$ , which equals $256$ . So, the denominator becomes $256m^{20}$ .
Rewrite Expression with Denominator: Rewrite the expression with the calculated denominator. $\newline$ Now we have $(\frac{2m^{9}}{256m^{20}})$ .
Simplify Fraction: Simplify the fraction by dividing the coefficients and subtracting the exponents. $\newline$ Divide the coefficients: $\frac{2}{256} = \frac{1}{128}$ . $\newline$ Subtract the exponents: $m^{(9-20)} = m^{-11}$ .
Final Expression: Write the final expression using only positive exponents. $\newline$ Since we cannot have negative exponents in the final answer, we express $m^{-11}$ as $1/m^{11}$ . $\newline$ The final expression is $(1/128)*(1/m^{11})$ or $1/(128m^{11})$ .

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