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$Express the following fraction in simplest form, only using positive exponents. (2q^(-1)j^(6))/((3q^(-1)j^(2))^(-1)) Answer:$

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{2 q^{-1} j^{6}}{\left(3 q^{-1} j^{2}\right)^{-1}}$ $\newline$ 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{2 q^{-1} j^{6}}{\left(3 q^{-1} j^{2}\right)^{-1}}

\newline

Answer:

Simplify Denominator: We start by simplifying the denominator which has a negative exponent. To do this, we flip the fraction inside the parentheses and change the negative exponent to a positive one. $\newline$ $(3q^{-1}j^{2})^{-1}$ becomes $3^{-1}q^{1}j^{-2}$
Rewrite Expression: Now we rewrite the entire expression with the simplified denominator: $\newline$ egin{equation}( $2$ q^{ $-1$ }j^{ $6$ }) * ( $3$ ^{ $-1$ }q^{ $1$ }j^{ $-2$ }) $\newline$ egin{equation}
Multiply Terms: Next, we simplify the expression by multiplying the terms with the same base and adding their exponents: $2 \times 3^{-1} \times q^{-1+1} \times j^{6-2}$
Simplify Exponents: We simplify the exponents: $\newline$ $2 \times 3^{-1} \times q^{0} \times j^{4}$ $\newline$ Since $q^{0}$ equals $1$ , we can remove it from the expression: $\newline$ $2 \times 3^{-1} \times j^{4}$
Convert Negative Exponent: Now we convert the negative exponent for $3$ to a positive exponent by writing it as a fraction: $\newline$ $2 \times \left(\frac{1}{3}\right) \times j^{4}$
Multiply Coefficients: Finally, we multiply the coefficients $(2 \text{ and } \frac{1}{3})$ and keep the $j$ term as is: $\newline$ $(\frac{2}{1}) \times (\frac{1}{3}) \times j^{4}$
Final Simplification: Perform the multiplication of the coefficients: $\newline$ $(\frac{2}{3}) \times j^{4}$ $\newline$ This is the simplest form of the expression using only positive exponents.

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