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$Express the following fraction in simplest form, only using positive exponents. (15r^(9))/((3j^(-2)r^(5))^(-1)) Answer:$

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{15 r^{9}}{\left(3 j^{-2} r^{5}\right)^{-1}}$ $\newline$ 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{15 r^{9}}{\left(3 j^{-2} r^{5}\right)^{-1}}

\newline

Answer:

Write Expression, Identify Exponent: Write down the given expression and identify the negative exponent. $\newline$ The given expression is $(15r^{9})/((3j^{-2}r^{5})^{-1})$ . $\newline$ We need to simplify this expression and express it with only positive exponents.
Apply Negative Exponent Rule: Apply the negative exponent rule to the denominator. $\newline$ The negative exponent rule states that $a^{-n} = \frac{1}{a^n}$ . We will apply this rule to the denominator. $\newline$ $\frac{15r^{9}}{(3j^{-2}r^{5})^{-1}} = (15r^{9})(3j^{-2}r^{5})$
Simplify Expression, Apply Rule: Simplify the expression by applying the negative exponent rule to $j^{-2}$ . We will now convert $j^{-2}$ to its positive exponent form. $(15r^{9})*(3j^{-2}r^{5}) = (15r^{9})*(3*(1/j^2)*r^{5})$
Multiply Terms: Multiply the terms. $\newline$ Now we multiply the terms together. $\newline$ $(15r^{9})\cdot(3\cdot(\frac{1}{j^2})\cdot r^{5}) = 15\cdot 3\cdot r^{9}\cdot r^{5}/j^2$
Combine Like Terms: Combine the like terms. $\newline$ We will combine the $r$ terms by adding their exponents since they have the same base. $\newline$ $15 \times 3 \times r^{9+5} / j^2 = 45 \times r^{14} / j^2$
Write Final Expression: Write the final simplified expression. $\newline$ The final expression in simplest form with only positive exponents is: $\newline$ $\frac{45r^{14}}{j^2}$

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