Express the given expression without logs, in simplest form. Assume all variables represent positive values. (11^(log_(11)(7sqrtw)-log_(11)(9y^(2)))) Answer:

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Express the given expression without logs, in simplest form. Assume all variables represent positive values.  (11^(log_(11)(7sqrtw)-log_(11)(9y^(2)))) Answer:

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Recognize Properties: Recognize the properties of logarithms that will be used to simplify the expression. The expression involves the laws of logarithms, specifically the quotient rule which states that log_b(a) - log_b(c) = log_b(a/c). We will use this property to combine the logarithms in the exponent.Apply Quotient Rule: Apply the quotient rule to the logarithms in the exponent. Using the quotient rule, we can rewrite log_(11)(7sqrt(w)) - log_(11)(9y^2) as log_(11)((7sqrt(w))/(9y^2)).Simplify Expression: Simplify the expression inside the logarithm. The expression inside the logarithm can be simplified by recognizing that sqrt(w) is w^(1/2). So, we have log_(11)((7w^(1/2))/(9y^2)).Apply Power Rule: Apply the power rule of exponents to the base 11 with the logarithm as the exponent. According to the power rule, b^(log_b(x)) = x for any base b and positive x. Therefore, 11^(log_(11)((7w^(1/2))/(9y^2))) simplifies to (7w^(1/2))/(9y^2).Check Simplified Form: Check if the expression is in its simplest form. The expression (7w^(1/2))/(9y^2) is already in its simplest form, as there are no common factors that can be cancelled out between the numerator and the denominator.

Express the given expression without logs, in simplest form. Assume all variables represent positive values. $\newline$ $\left(11^{\log _{11}(7 \sqrt{w})-\log _{11}\left(9 y^{2}\right)}\right)$ $\newline$ Answer:

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Express the given expression without logs, in simplest form. Assume all variables represent positive values. $\newline$ $\left(11^{\log _{11}(7 \sqrt{w})-\log _{11}\left(9 y^{2}\right)}\right)$ $\newline$ Answer: