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$Express the following fraction in simplest form using only positive exponents. (3c^(7))/(3(c^(3))^(3)) Answer:$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{3 c^{7}}{3\left(c^{3}\right)^{3}}$ $\newline$ 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{3 c^{7}}{3\left(c^{3}\right)^{3}}

\newline

Answer:

Write Expression: Write down the given expression. $\newline$ We have the expression $(\frac{3c^{7}}{3(c^{3})^{3}})$ .
Simplify Denominator: Simplify the denominator. $\newline$ The denominator has a power raised to a power, which means we multiply the exponents. So, $(c^{3})^{3}$ becomes $c^{3*3}$ which is $c^{9}$ .
Rewrite with Simplified Denominator: Rewrite the expression with the simplified denominator. $\newline$ Now the expression is $(3c^{7})/(3c^{9})$ .
Cancel Common Factors: Cancel out the common factors in the numerator and the denominator. $\newline$ The number $3$ in the numerator and denominator cancels out. We are left with $c^{7}/c^{9}$ .
Apply Division Rule: Apply the rule for dividing powers with the same base. $\newline$ When dividing powers with the same base, subtract the exponents: $c^{7}/c^{9} = c^{7-9} = c^{-2}$ .
Express Negative Exponent: Express the negative exponent as a positive exponent. Since we want only positive exponents, we write $c^{-2}$ as $1/c^{2}$ .

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