Express the following fraction in simplest form, only using positive exponents. (5(r^(4))^(3))/(-20r^(-3)) Answer:

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Express the following fraction in simplest form, only using positive exponents.  (5(r^(4))^(3))/(-20r^(-3)) Answer:

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Identify negative exponent: Write down the given expression and identify the negative exponent. The given expression is (5(r^(4))^(3))/(-20r^(-3)). We have a negative exponent in the denominator which is r^(-3).Apply power of power rule: Apply the power of a power rule to the numerator. The power of a power rule states that (a^(m))^n = a^(m*n). So, (r^(4))^3 = r^(4*3) = r^(12). Now the expression becomes (5r^(12))/(-20r^(-3)).Convert negative exponent: Convert the negative exponent to a positive exponent by moving the term to the numerator. According to the exponent rules, a^(-n) = 1/a^n when moving from the denominator to the numerator. So, r^(-3) becomes r^(3) when moved to the numerator. Now the expression becomes (5r^(12) * r^(3))/(-20).Combine like terms: Combine the like terms in the numerator using the product of powers rule. The product of powers rule states that a^(m) * a^(n) = a^(m+n). So, r^(12) * r^(3) = r^(12+3) = r^(15). Now the expression becomes (5r^(15))/(-20).Simplify fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 5 and 20 is 5. Divide both the numerator and the denominator by 5. (5/5)r^(15) / (-20/5) = r^(15) / (-4).Make denominator positive: Since we cannot have a negative in the denominator, we can multiply the numerator and the denominator by -1 to make the denominator positive. Multiplying by -1, we get (-1 * r^(15)) / (-1 * -4) = -r^(15) / 4.

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{5\left(r^{4}\right)^{3}}{-20 r^{-3}}$ $\newline$ Answer:

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Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{5\left(r^{4}\right)^{3}}{-20 r^{-3}}$ $\newline$ Answer: