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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. $\newline$ $\frac{(-6 a)^{2}}{(5 b)^{4}}$ $\newline$ $a=-5 \text { and } b=-6$ $\newline$ $\frac{1}{900}$ $\newline$ $\frac{1}{1800}$ $\newline$ $-\frac{1}{900}$ $\newline$ $-\frac{1}{1800}$

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Multiplication with rational exponents

Full solution

Q. Select the answer which is equivalent to the given expression using your calculator.

\newline

\frac{(-6 a)^{2}}{(5 b)^{4}}

\newline

a=-5 \text { and } b=-6

\newline

\frac{1}{900}

\newline

\frac{1}{1800}

\newline

-\frac{1}{900}

\newline

-\frac{1}{1800}

Substitute values: Substitute the given values of $a$ and $b$ into the expression. $\frac{(-6a)^{2}}{(5b)^{4}}$ with $a = -5$ and $b = -6$ becomes $\frac{(-6*(-5))^{2}}{(5*(-6))^{4}}$ .
Calculate values: Calculate the value of $(-6*(-5))$ and $(5*(-6))$ . $-6 \times -5 = 30$ and $5 \times -6 = -30$ .
Raise to powers: Raise the results to the respective powers. $\newline$ $(30)^{2}$ and $(-30)^{4}$ .
Calculate powers: Calculate the powers. $30^2 = 900$ and $(-30)^4 = 810000$ .
Divide results: Divide the results. $\frac{900}{810000}.$
Simplify division: Simplify the division. $900 / 810000 = 1 / 900$ .
Check sign: Check the sign of the result. $\newline$ Since both the numerator and the denominator are positive, the result is positive.

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