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

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

\newline

Answer:

Identify Base and Exponents: Write down the given expression and identify the base and exponents. $\newline$ The given expression is $(2(s^{3})^{2})/(3s)$ . We have a power to a power for the term $s^{3}$ raised to the power of $2$ , and we have a multiplication of $2$ with this term in the numerator. In the denominator, we have the product of $3$ and $s$ .
Apply Power of Power Rule: Apply the power of a power rule to the term $(s^{3})^{2}$ . $\newline$ According to the power of a power rule, $(a^{m})^{n} = a^{m*n}$ . Therefore, $(s^{3})^{2} = s^{3*2} = s^{6}$ .
Rewrite with Simplified Exponent: Rewrite the expression with the simplified exponent for $s$ . Now the expression becomes $\frac{2\cdot s^{6}}{3s}$ .
Divide Terms with Common Base: Simplify the expression by dividing the terms with the common base $s$ . Since $s^{6}$ in the numerator and $s$ in the denominator have the same base, we can simplify by subtracting the exponents: $\frac{s^{6}}{s} = s^{6-1} = s^{5}$ .
Write Simplified Expression: Write the simplified expression. $\newline$ After simplifying, the expression is now $(\frac{2s^{5}}{3})$ .
Check for Further Simplification: Check if the expression can be simplified further. $\newline$ The expression $(\frac{2s^{5}}{3})$ is already in its simplest form. There are no common factors between the numerator and the denominator that can be cancelled out, and all exponents are positive.

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