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$Express the following fraction in simplest form using only positive exponents. (2(q^(5))^(3))/(10q^(10)) Answer:$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{2\left(q^{5}\right)^{3}}{10 q^{10}}$ $\newline$ 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(q^{5}\right)^{3}}{10 q^{10}}

\newline

Answer:

Apply Power of Power Rule: Simplify the numerator using the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{m*n}$ . We apply this rule to the numerator. $\newline$ $(2(q^{5})^{3}) = 2 \times (q^{5*3}) = 2 \times q^{15}$
Divide Numerator by Denominator: Simplify the fraction by dividing the numerator by the denominator. $\newline$ We have the fraction $(2 \cdot q^{15}) / (10 \cdot q^{10})$ . To simplify, we divide both the coefficients $(2/10)$ and the $q$ terms $(q^{15}/q^{10})$ . $\newline$ $(2/10)$ simplifies to $1/5$ , since $2$ and $10$ have a common factor of $2$ . $\newline$ $(q^{15}/q^{10})$ simplifies to $(2/10)$ $0$ , using the quotient of powers rule which states that $(2/10)$ $1$ when $(2/10)$ $2$ .
Write Final Simplified Fraction: Write the simplified fraction. $\newline$ After simplifying both parts, we combine them to get the final simplified fraction. $\newline$ $(\frac{1}{5}) \cdot q^5$

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