Simplify the following expression to simplest form using only positive exponents. (27x^(-9)y^(18))^(-(5)/(3)) Answer:

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Simplify the following expression to simplest form using only positive exponents.  (27x^(-9)y^(18))^(-(5)/(3)) Answer:

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Apply negative exponent rule: Apply the negative exponent rule to the entire expression. The negative exponent rule states that a^(-n) = 1/(a^n). We will apply this rule to the entire expression (27x^(-9)y^(18))^(-(5)/(3)).Rewrite with positive exponents: Rewrite the expression with positive exponents by taking the reciprocal. Taking the reciprocal of the base and making the exponent positive, we get: (1/(27x^(-9)y^(18)))^(5/3)Apply power rule: Apply the power rule to the expression inside the parentheses. The power rule states that (a^m)^n = a^(m*n). We will apply this rule to each part of the expression inside the parentheses. (1/27)^(5/3) * (x^(-9))^(5/3) * (y^(18))^(5/3)Simplify each part: Simplify each part of the expression separately. Simplify (1/27)^(5/3), (x^(-9))^(5/3), and (y^(18))^(5/3) by multiplying the exponents. (1/27)^(5/3) = 1/(27^(5/3)) (x^(-9))^(5/3) = x^((-9)*(5/3)) = x^(-15) (y^(18))^(5/3) = y^((18)*(5/3)) = y^(30)Calculate 27^(5/3): Calculate the value of 27^(5/3). 27 is 3^3, so we can rewrite 27^(5/3) as (3^3)^(5/3). (3^3)^(5/3) = 3^(3*(5/3)) = 3^5 = 243 Therefore, 1/(27^(5/3)) = 1/243Combine simplified parts: Combine the simplified parts into one expression. Combine the results from the previous steps to get the final expression with positive exponents. 1/243 * x^(-15) * y^(30)Rewrite x^(-15): Rewrite x^(-15) with a positive exponent. To rewrite x^(-15) with a positive exponent, we take the reciprocal of x to the power of 15. 1/243 * 1/(x^(15)) * y^(30)Combine the fractions: Combine the fractions. Combine the fractions to get a single fraction. 1/(243x^(15)) * y^(30)Write final expression: Write the final simplified expression. The final simplified expression is: y^(30) / (243x^(15))

Simplify the following expression to simplest form using only positive exponents. $\newline$ $\left(27 x^{-9} y^{18}\right)^{-\frac{5}{3}}$ $\newline$ Answer:

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Simplify the following expression to simplest form using only positive exponents. $\newline$ $\left(27 x^{-9} y^{18}\right)^{-\frac{5}{3}}$ $\newline$ Answer: