Express the following fraction in simplest form, only using positive exponents. (-2j^(9))/(-5(j^(-1))^(3)) Answer:

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Express the following fraction in simplest form, only using positive exponents.  (-2j^(9))/(-5(j^(-1))^(3)) Answer:

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Write & Identify Negative Exponent: Write down the given expression and identify the negative exponent. The given expression is (-2j^(9))/(-5(j^(-1))^(3)). We need to simplify this expression and express it with only positive exponents.Simplify Denominator: Simplify the denominator. The denominator is -5(j^(-1))^(3). We need to apply the power to a power rule, which states that (a^(m))^n = a^(m*n). So, (j^(-1))^(3) = j^(-1*3) = j^(-3). Now the expression becomes (-2j^(9))/(-5j^(-3)).Convert Negative to Positive Exponent: Convert the negative exponent to a positive exponent. To convert a negative exponent to a positive exponent, we use the rule that a^(-n) = 1/(a^n). So, j^(-3) = 1/(j^3). Now the expression becomes (-2j^(9))/(-5 * 1/(j^3)).Multiply by Reciprocal: Multiply the numerator by the reciprocal of the denominator. To divide by a fraction, we multiply by its reciprocal. So we multiply -2j^(9) by the reciprocal of -5 * 1/(j^3), which is -1/(5j^3). The expression becomes (-2j^(9)) * (-1/(5j^3)).Simplify by Multiplying Numerators: Simplify the expression by multiplying the numerators and denominators. When we multiply fractions, we multiply the numerators together and the denominators together. The expression becomes (-2 * -1) * (j^(9) / (5j^3)).Simplify Constants & Apply Quotient Rule: Simplify the constants and apply the quotient rule for exponents. The constants simplify to 2 * 1 = 2. The quotient rule for exponents states that a^(m) / a^(n) = a^(m-n) when m > n. So, j^(9) / j^(3) = j^(9-3) = j^(6). Now the expression becomes 2 * j^(6) / 5.Write Final Simplified Expression: Write the final simplified expression. The final simplified expression is 2j^(6) / 5.

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{-2 j^{9}}{-5\left(j^{-1}\right)^{3}}$ $\newline$ Answer:

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Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{-2 j^{9}}{-5\left(j^{-1}\right)^{3}}$ $\newline$ Answer: