Simplify the following expression to simplest form using only positive exponents. (8x^(-15)y^(18))^(-(5)/(3)) Answer:

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Simplify the following expression to simplest form using only positive exponents.  (8x^(-15)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 (8x^(-15)y^(18))^(-(5)/(3)).Distribute exponents to factors: Distribute the exponent to each factor inside the parentheses. When raising a power to a power, you multiply the exponents. In this case, we have a product inside the parentheses, so we will distribute the exponent to each factor. (8^(-(5)/(3))) * (x^(-15))^(-(5)/(3)) * (y^(18))^(-(5)/(3))Multiply exponents for each factor: Multiply the exponents for each factor. Now we multiply the exponents for each factor. 8^(-5/3) becomes 8^(5/3) because the negative sign is canceled by the negative exponent outside. x^(-15 * -5/3) becomes x^(75/3) because -15 * -5/3 is 75/3. y^(18 * -5/3) becomes y^(-30) because 18 * -5/3 is -30.Simplify exponents: Simplify the exponents. Simplify the exponents by dividing 75 by 3 for the x term and by recognizing that y^(-30) can be written with a positive exponent by taking its reciprocal. 8^(5/3), x^(75/3) becomes x^(25), y^(-30) becomes 1/(y^(30))Write with positive exponents: Write the expression with only positive exponents. We want to express everything with positive exponents, so we will write y^(-30) as its reciprocal. 8^(5/3) * x^(25) * 1/(y^(30))Simplify 8^(5/3): Simplify the expression for 8^(5/3). 8 is 2^3, so we can rewrite 8^(5/3) as (2^3)^(5/3). When raising a power to a power, we multiply the exponents. (2^3)^(5/3) = 2^(3*(5/3)) = 2^5Combine simplified terms: Combine all the simplified terms. Now we combine all the terms to get the final expression. 2^5 * x^(25) / y^(30)Calculate 2^5: Calculate the value of 2^5. 2^5 is 2 multiplied by itself 5 times, which equals 32. 32 * x^(25) / y^(30)

Simplify the following expression to simplest form using only positive exponents. $\newline$ $\left(8 x^{-15} y^{18}\right)^{-\frac{5}{3}}$ $\newline$ Answer:

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Simplify the following expression to simplest form using only positive exponents. $\newline$ $\left(8 x^{-15} y^{18}\right)^{-\frac{5}{3}}$ $\newline$ Answer: