Select the answer which is equivalent to the given expression using your calculator. {:[(2a^(-3))/(-8b^(-4))],[a=-6" and "b=3]:} -(3)/(32) (3)/(32) (3)/(8) -(3)/(8)

Question

Select the answer which is equivalent to the given expression using your calculator.  {:[(2a^(-3))/(-8b^(-4))],[a=-6" and "b=3]:}  -(3)/(32)  (3)/(32)  (3)/(8)  -(3)/(8)

Bytelearn · Accepted Answer

Write Expression and Substitute Values: First, let's write down the given expression and substitute the values of $ a $ and $ b $ into the expression. The expression is $\frac{2a^{-3}}{-8b^{-4}}$, where $ a = -6 $ and $ b = 3 $. Substituting the values, we get $\frac{2(-6)^{-3}}{-8(3)^{-4}}$.Simplify Expression Step by Step: Now, let's simplify the expression step by step. First, we calculate $ (-6)^{-3} $ and $ (3)^{-4} $. $ (-6)^{-3} $ means $ \frac{1}{(-6)^3} $, which is $ \frac{1}{-216} $. $ (3)^{-4} $ means $ \frac{1}{3^4} $, which is $ \frac{1}{81} $. So the expression becomes $\frac{2 \cdot \frac{1}{-216}}{-8 \cdot \frac{1}{81}}$.Simplify Fractions: Next, we simplify the fractions by multiplying the numerators and denominators. The expression simplifies to $\frac{2}{-216} \cdot \frac{81}{-8}$.Multiply Numerators and Denominators: Now, we multiply the numerators together and the denominators together. $ 2 \cdot 81 = 162 $ and $ -216 \cdot -8 = 1728 $. So the expression becomes $\frac{162}{1728}$.Simplify Fraction with GCD: We can simplify the fraction $\frac{162}{1728}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 162. $ \frac{162}{162} = 1 $ and $ \frac{1728}{162} = 10.5 $. However, this step contains a math error because 162 is not the greatest common divisor of 162 and 1728.

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\begin{array}{c} \frac{2 a^{-3}}{-8 b^{-4}} \\ a=-6 \text { and } b=3 \end{array}$ $\newline$ $-\frac{3}{32}$ $\newline$ $\frac{3}{32}$ $\newline$ $\frac{3}{8}$ $\newline$ $-\frac{3}{8}$

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