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

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

\newline

Answer:

Simplify Denominator: Simplify the denominator. $\newline$ The denominator is $(-3(n^{5})^{3})$ . We need to apply the power of a power rule, which states that $(a^{m})^{n} = a^{m*n}$ . $\newline$ So, $(-3(n^{5})^{3}) = -3 \times n^{5*3} = -3 \times n^{15}.$
Rewrite Fraction: Rewrite the fraction with the simplified denominator. The fraction is now $(-3n^{-3})/(-3 \cdot n^{15})$ .
Cancel Common Factor: Cancel out the common factor of $-3$ in the numerator and the denominator. $\newline$ $(-3n^{-3})/(-3 \cdot n^{15}) = n^{-3}/n^{15}$ .
Apply Quotient Rule: Apply the quotient rule for exponents. $\newline$ The quotient rule states that $a^{m}/a^{n} = a^{m-n}$ when $a \neq 0$ . $\newline$ So, $n^{-3}/n^{15} = n^{-3-15} = n^{-18}.$
Express Positive Exponent: Express the negative exponent as a positive exponent. $\newline$ To express $n^{-18}$ with a positive exponent, we write it as $1/n^{18}$ .

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