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$Express the following fraction in simplest form using only positive exponents. ((3j^(5))^(2))/(2j^(8)) Answer:$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{\left(3 j^{5}\right)^{2}}{2 j^{8}}$ $\newline$ 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{\left(3 j^{5}\right)^{2}}{2 j^{8}}

\newline

Answer:

Apply Power Rule: Apply the power of a power rule to the numerator. $\newline$ The power of a power rule states that $(a^m)^n = a^{m*n}$ . We will apply this rule to the numerator $(3j^{5})^{2}$ . $\newline$ $(3j^{5})^{2} = 3^{2} \times (j^{5})^{2} = 3^{2} \times j^{10}$
Rewrite with Simplified Numerator: Rewrite the expression with the simplified numerator. $\newline$ Now we have the expression: $\newline$ $(3^{2} \cdot j^{10}) / (2j^{8})$
Simplify Numerical Part: Simplify the numerical part of the numerator. $\newline$ Calculate $3^{2}$ which is $3 \times 3 = 9$ . $\newline$ So, the expression becomes: $\newline$ $\frac{9 \times j^{10}}{2j^{8}}$
Apply Quotient of Powers Rule: Apply the quotient of powers rule to the variable part. $\newline$ The quotient of powers rule states that $a^{m}/a^{n} = a^{m-n}$ when m > n. We will apply this rule to $j^{10} / j^{8}$ . $\newline$ $j^{10} / j^{8} = j^{10-8} = j^{2}$
Rewrite with Simplified Variable Part: Rewrite the expression with the simplified variable part. $\newline$ Now we have the expression: $\newline$ $(9 \cdot j^{2}) / 2$ $\newline$ Since there are no $j$ terms in the denominator to simplify further, this is the simplest form of the expression.
Check for Simplification: Check if the expression is fully simplified and only contains positive exponents. The expression $(9 \cdot j^{2}) / 2$ is fully simplified and contains only positive exponents.

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