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$Express the following fraction in simplest form using only positive exponents. (2d^(4))/(5(d^(4))^(3)) Answer: Submit Answer$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{2 d^{4}}{5\left(d^{4}\right)^{3}}$ $\newline$ 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.

\newline

\frac{2 d^{4}}{5\left(d^{4}\right)^{3}}

\newline

Answer:

\newline

Submit Answer

Write Expression: Write down the given expression. $\newline$ We have the expression $(\frac{2d^{4}}{5(d^{4})^{3}})$ .
Apply Power Rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^{m})^{n} = a^{m*n}$ . So, we apply this rule to $(d^{4})^{3}$ . $\newline$ $(d^{4})^{3} = d^{4*3} = d^{12}$ .
Substitute Exponent: Substitute the simplified exponent back into the original expression. $\newline$ Now we have $(2d^{4})/(5d^{12})$ .
Simplify Expression: Simplify the expression by canceling out common factors. $\newline$ Since $d^{4}$ is a factor in both the numerator and the denominator, we can simplify the expression by dividing both by $d^{4}$ . $\newline$ $\frac{2d^{4}}{5d^{12}} = \frac{2}{5d^{12-4}} = \frac{2}{5d^{8}}$ .
Write Final Answer: Write the final simplified expression. $\newline$ The expression is now fully simplified, and all exponents are positive. $\newline$ The final answer is $(\frac{2}{5d^{8}})$ .

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