Express the following fraction in simplest form, only using positive exponents. (20a^(7))/(-4(a^(-2))^(2)) Answer:

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Express the following fraction in simplest form, only using positive exponents.  (20a^(7))/(-4(a^(-2))^(2)) Answer:

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Simplify Denominator: Simplify the denominator. The denominator is -4(a^(-2))^2. We need to apply the power of a power rule, which states that (a^m)^n = a^(m*n). So, (a^(-2))^2 = a^(-2*2) = a^(-4). Calculation: -4(a^(-2))^2 = -4 * a^(-4)Rewrite Negative Exponent: Rewrite the negative exponent as a positive exponent. To convert a negative exponent to a positive exponent, we use the rule a^(-n) = 1/a^n. So, a^(-4) becomes 1/a^4. Calculation: -4 * a^(-4) = -4 * (1/a^4)Divide Numerator by Denominator: Simplify the fraction by dividing the numerator by the denominator. Now we divide 20a^7 by -4 * (1/a^4). This is the same as multiplying 20a^7 by the reciprocal of the denominator. Calculation: (20a^7) / (-4 * (1/a^4)) = 20a^7 * (-1/4) * a^4Multiply Coefficients and Variables: Multiply the coefficients and the variables separately. We multiply the coefficients 20 and -1/4, and then we use the property of exponents a^m * a^n = a^(m+n) to multiply a^7 and a^4. Calculation: 20 * (-1/4) = -5 and a^7 * a^4 = a^(7+4) = a^11Combine Results: Combine the results to get the final answer. We combine the coefficient -5 with the variable part a^11. Calculation: -5 * a^11

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{20 a^{7}}{-4\left(a^{-2}\right)^{2}}$ $\newline$ Answer:

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Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{20 a^{7}}{-4\left(a^{-2}\right)^{2}}$ $\newline$ Answer: