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$Express the following fraction in simplest form using only positive exponents. ((5b^(3))^(2))/(5b^(6)) Answer:$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{\left(5 b^{3}\right)^{2}}{5 b^{6}}$ $\newline$ 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(5 b^{3}\right)^{2}}{5 b^{6}}

\newline

Answer:

Write Expression: Write down the given expression. $\newline$ We have the expression $\frac{(5b^{3})^{2}}{5b^{6}}$ .
Apply Power Rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{m*n}$ . So we apply this rule to the numerator. $\newline$ $((5b^{3})^{2}) = 5^{2} \times (b^{3})^{2} = 25b^{3*2} = 25b^{6}$ .
Rewrite with Simplified Numerator: Rewrite the expression with the simplified numerator. $\newline$ Now the expression is $(25b^{6})/(5b^{6})$ .
Simplify Fraction: Simplify the fraction by dividing both the numerator and the denominator by the common terms. $\newline$ Since $25b^{6}$ and $5b^{6}$ both have the common term $5b^{6}$ , we can divide them by $5b^{6}$ . $\newline$ $\frac{25b^{6}}{5b^{6}} = \frac{25}{5} \times \frac{b^{6}}{b^{6}} = 5 \times 1 = 5$ .
Check for Remaining Simplifications: Check for any remaining simplifications. There are no more $b$ terms in the denominator, and the numerical part of the fraction is already in its simplest form.

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