Express the following fraction in simplest form, only using positive exponents. ((3k^(3)v^(2))^(-5))/(4k^(7)v^(5)) Answer:

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Express the following fraction in simplest form, only using positive exponents.  ((3k^(3)v^(2))^(-5))/(4k^(7)v^(5)) Answer:

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Apply negative exponent rule: Apply the negative exponent rule to the numerator. The negative exponent rule states that a^(-n) = 1/(a^n). We will apply this rule to the numerator to make the exponent positive. ((3k^(3)v^(2))^(-5)) = 1/((3k^(3)v^(2))^(5))Expand numerator exponent: Expand the exponent in the numerator. When raising a power to a power, you multiply the exponents. We will apply this to each factor in the numerator. 1/((3k^(3)v^(2))^(5)) = 1/(3^5 * (k^(3))^5 * (v^(2))^5)Calculate powers in numerator: Calculate the powers in the numerator. Now we will calculate each of the powers separately. 1/(3^5 * (k^(3))^5 * (v^(2))^5) = 1/(243 * k^(15) * v^(10))Combine numerator and denominator: Combine the numerator and the denominator. Now we will write the entire fraction with the expanded numerator and the original denominator. 1/(243 * k^(15) * v^(10)) / (4k^(7)v^(5))Simplify fraction by dividing: Simplify the fraction by dividing the numerator by the denominator. To divide two fractions, you multiply the first fraction by the reciprocal of the second fraction. (1/(243 * k^(15) * v^(10))) * (1/(4k^(7)v^(5)))Multiply the fractions: Multiply the fractions. Now we will multiply the numerators and the denominators separately. (1 * 1) / (243 * k^(15) * v^(10) * 4k^(7) * v^(5))Combine like terms in denominator: Combine like terms in the denominator. We will add the exponents of like bases in the denominator. 1 / (243 * 4 * k^(15+7) * v^(10+5))Calculate exponents and coefficients: Calculate the exponents and coefficients in the denominator. Now we will calculate the exponents and multiply the coefficients. 1 / (972 * k^(22) * v^(15))Write final answer: Write the final answer with positive exponents. The fraction is already in simplest form with positive exponents. 1 / (972 * k^(22) * v^(15))

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{\left(3 k^{3} v^{2}\right)^{-5}}{4 k^{7} v^{5}}$ $\newline$ Answer:

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Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{\left(3 k^{3} v^{2}\right)^{-5}}{4 k^{7} v^{5}}$ $\newline$ Answer: