Simplify the following expression to simplest form using only positive exponents. (9x^(8)y^(-12))^(-(1)/(2)) Answer:

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Simplify the following expression to simplest form using only positive exponents.  (9x^(8)y^(-12))^(-(1)/(2)) 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 expression (9x^(8)y^(-12))^(-(1)/(2)).Rewrite with Positive Exponent: Rewrite the expression with a positive exponent by taking the reciprocal. (9x^(8)y^(-12))^(-(1)/(2)) becomes 1/((9x^(8)y^(-12))^(1/2))Apply Power of Power Rule: Apply the power of a power rule. The power of a 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/((9^(1/2))(x^(8*(1/2)))(y^(-12*(1/2))))Simplify Exponents: Simplify the exponents. Calculate the new exponents by multiplying the exponents. 1/((9^(1/2))(x^(4))(y^(-6)))Simplify Square Root: Simplify the square root of 9. The square root of 9 is 3. 1/((3)(x^(4))(y^(-6)))Rewrite Negative Exponent: Rewrite the negative exponent as a positive exponent in the denominator. The negative exponent rule states that a^(-n) = 1/(a^n). We will apply this rule to y^(-6). 1/((3)(x^(4))(1/(y^(6))))Simplify Expression: Simplify the expression by multiplying the denominators. When we multiply fractions, we multiply the numerators and the denominators separately. 1/((3)(x^(4)))*(y^(6))Combine Denominator: Combine the terms in the denominator. Since 3 and x^(4) are already in the denominator, we just need to multiply them by y^(6). 1/((3x^(4)y^(6)))

Simplify the following expression to simplest form using only positive exponents. $\newline$ $\left(9 x^{8} y^{-12}\right)^{-\frac{1}{2}}$ $\newline$ Answer:

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Simplify the following expression to simplest form using only positive exponents. $\newline$ $\left(9 x^{8} y^{-12}\right)^{-\frac{1}{2}}$ $\newline$ Answer: