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Select the answer which is equivalent to the given expression using your calculator. ((-6a)^(2))/((5b)^(4)) a=-5" and "b=-6 (1)/(900) (1)/(1800) -(1)/(900) -(1)/(1800)

Select the answer which is equivalent to the given expression using your calculator.\newline(−6a)2(5b)4 \frac{(-6 a)^{2}}{(5 b)^{4}} \newlinea=−5 and b=−6 a=-5 \text { and } b=-6 \newline1900 \frac{1}{900} \newline11800 \frac{1}{1800} \newline−1900 -\frac{1}{900} \newline−11800 -\frac{1}{1800}

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Full solution

Q. Select the answer which is equivalent to the given expression using your calculator.\newline(−6a)2(5b)4 \frac{(-6 a)^{2}}{(5 b)^{4}} \newlinea=−5 and b=−6 a=-5 \text { and } b=-6 \newline1900 \frac{1}{900} \newline11800 \frac{1}{1800} \newline−1900 -\frac{1}{900} \newline−11800 -\frac{1}{1800}
  1. Substitute values: Substitute the given values of aa and bb into the expression.(−6a)2(5b)4\frac{(-6a)^{2}}{(5b)^{4}} with a=−5a = -5 and b=−6b = -6 becomes (−6∗(−5))2(5∗(−6))4\frac{(-6*(-5))^{2}}{(5*(-6))^{4}}.
  2. Calculate values: Calculate the value of (−6∗(−5))(-6*(-5)) and (5∗(−6))(5*(-6)).−6×−5=30-6 \times -5 = 30 and 5×−6=−305 \times -6 = -30.
  3. Raise to powers: Raise the results to the respective powers.\newline(30)2(30)^{2} and (−30)4(-30)^{4}.
  4. Calculate powers: Calculate the powers. 302=90030^2 = 900 and (−30)4=810000(-30)^4 = 810000.
  5. Divide results: Divide the results. 900810000.\frac{900}{810000}.
  6. Simplify division: Simplify the division. 900/810000=1/900900 / 810000 = 1 / 900.
  7. Check sign: Check the sign of the result.\newlineSince both the numerator and the denominator are positive, the result is positive.

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