Express the following fraction in simplest form using only positive exponents. (3w^(9))/(3(w^(3))^(5)) Answer:

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Express the following fraction in simplest form using only positive exponents.  (3w^(9))/(3(w^(3))^(5)) Answer:

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Write & Identify Properties: Write down the given expression and identify the properties of exponents that can be applied. Given expression: (3w^(9))/(3(w^(3))^(5)) We can apply the power of a power property for the denominator, which states that (a^(m))^n = a^(m*n).Apply Power of Power: Apply the power of a power property to the denominator. (3(w^(3))^(5)) = 3 * w^(3*5) = 3 * w^(15)Rewrite with Simplified Denominator: Rewrite the original expression with the simplified denominator. (3w^(9))/(3(w^(3))^(5)) = (3w^(9))/(3 * w^(15))Simplify by Canceling Factors: Simplify the expression by canceling out common factors in the numerator and the denominator. The common factor of 3 in the numerator and denominator can be canceled out, and we can use the quotient of powers property for the w terms, which states that a^(m)/a^(n) = a^(m-n) when a ≠ 0. (3w^(9))/(3 * w^(15)) = w^(9-15) = w^(-6)Rewrite with Positive Exponents: Since we need the expression with only positive exponents, we rewrite w^(-6) using the property a^(-n) = 1/a^(n). w^(-6) = 1/w^(6)

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{3 w^{9}}{3\left(w^{3}\right)^{5}}$ $\newline$ Answer:

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Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{3 w^{9}}{3\left(w^{3}\right)^{5}}$ $\newline$ Answer: