Simplify the following expression to simplest form using only positive exponents. (8x^(-3)y^(-21))^((2)/(3)) Answer:

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Simplify the following expression to simplest form using only positive exponents.  (8x^(-3)y^(-21))^((2)/(3)) Answer:

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Apply Power to Factors: Apply the power to each factor inside the parentheses. To simplify the expression (8x^(-3)y^(-21))^(2/3), we need to apply the exponent of 2/3 to each factor inside the parentheses. This means we will raise 8 to the power of 2/3, x to the power of -3*(2/3), and y to the power of -21*(2/3).Simplify Exponents: Simplify the exponents. Raising 8 to the power of 2/3 means we are looking for the cube root of 8 squared. For x and y, we multiply the exponents by 2/3, which simplifies the negative exponents. 8^(2/3) = (2^3)^(2/3) = 2^(3*(2/3)) = 2^2 = 4 x^(-3*(2/3)) = x^(-2) y^(-21*(2/3)) = y^(-14)Convert Negative Exponents: Convert negative exponents to positive exponents. To express the expression using only positive exponents, we take the reciprocal of the base for the negative exponents. x^(-2) = 1/x^2 y^(-14) = 1/y^14Combine Results: Combine the results. Now we combine the results from the previous steps to write the expression with positive exponents only. 4 * (1/x^2) * (1/y^14) = 4/(x^2 * y^14)

Simplify the following expression to simplest form using only positive exponents. $\newline$ $\left(8 x^{-3} y^{-21}\right)^{\frac{2}{3}}$ $\newline$ Answer:

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Simplify the following expression to simplest form using only positive exponents. $\newline$ $\left(8 x^{-3} y^{-21}\right)^{\frac{2}{3}}$ $\newline$ Answer: