Select the answer which is equivalent to the given expression using your calculator. {:[((5a)^(3))/(5b^(2))],[a=-2" and "b=-3]:} (5000)/(9) -(5000)/(9) -(200)/(9) (200)/(9)

Question

Select the answer which is equivalent to the given expression using your calculator.  {:[((5a)^(3))/(5b^(2))],[a=-2" and "b=-3]:}  (5000)/(9)  -(5000)/(9)  -(200)/(9)  (200)/(9)

Bytelearn · Accepted Answer

Substitute values: Substitute the given values of a and b into the expression. ((5a)^(3))/(5b^(2)) becomes ((5*(-2))^(3))/(5*(-3)^(2)).Calculate numerator: Calculate the numerator (5*(-2))^3. First, calculate 5 * -2, which is -10. Then raise -10 to the power of 3. (-10)^3 = -10 * -10 * -10 = -1000.Calculate denominator: Calculate the denominator 5*(-3)^2. First, calculate (-3)^2, which is 9. Then multiply by 5. 5 * 9 = 45.Divide numerator by denominator: Divide the numerator by the denominator. -1000 / 45 simplifies to -(1000/45).Simplify fraction: Simplify the fraction -(1000/45) if possible. The fraction cannot be simplified further as 1000 and 45 have no common factors other than 1.Convert to decimal: Convert the fraction to a decimal to match the answer choices. -(1000/45) is approximately -22.2222, which does not match any of the answer choices directly. However, we can multiply both the numerator and denominator by 100 to get the equivalent fraction -(100000/4500).Simplify fraction: Simplify the fraction -(100000/4500). Divide both the numerator and the denominator by 100 to get -(1000/45), which is the same as our original fraction. This step was unnecessary and does not change the fraction, so we should look for a mistake in our previous steps.

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\begin{array}{c} \frac{(5 a)^{3}}{5 b^{2}} \\ a=-2 \text { and } b=-3 \end{array}$ $\newline$ $\frac{5000}{9}$ $\newline$ $-\frac{5000}{9}$ $\newline$ $-\frac{200}{9}$ $\newline$ $\frac{200}{9}$

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