Select the answer which is equivalent to the given expression using your calculator. (-10a^((3)/(2)))/((32 b)^((2)/(5))) a=16" and "b=243 (160)/(9) -(160)/(9) -(160)/(27) (160)/(27)

Question

Select the answer which is equivalent to the given expression using your calculator.  (-10a^((3)/(2)))/((32 b)^((2)/(5)))  a=16" and "b=243  (160)/(9)  -(160)/(9)  -(160)/(27)  (160)/(27)

Bytelearn · Accepted Answer

Substitute Given Values: First, let's substitute the given values of a and b into the expression. a = 16 b = 243 The expression becomes (-10 * 16^(3/2)) / (32 * 243^(2/5)).Simplify Exponents: Now, let's simplify the exponents. 16^(3/2) means the square root of 16 raised to the 3rd power. Since the square root of 16 is 4, we have (4^3). 243^(2/5) means the 5th root of 243 squared. Since the 5th root of 243 is 3, we have (3^2). The expression now is (-10 * 4^3) / (32 * 3^2).Calculate Powers: Next, we calculate the powers. 4^3 = 4 * 4 * 4 = 64 3^2 = 3 * 3 = 9 The expression simplifies to (-10 * 64) / (32 * 9).Multiply Numbers: Now, let's multiply the numbers. -10 * 64 = -640 32 * 9 = 288 The expression is now -640 / 288.Simplify Fraction: Finally, we simplify the fraction -640 / 288 by dividing both the numerator and the denominator by their greatest common divisor, which is 32. -640 / 32 = -20 288 / 32 = 9 The simplified expression is -20 / 9.

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\frac{-10 a^{\frac{3}{2}}}{(32 b)^{\frac{2}{5}}}$ $\newline$ $a=16 \text { and } b=243$ $\newline$ $\frac{160}{9}$ $\newline$ $-\frac{160}{9}$ $\newline$ $-\frac{160}{27}$ $\newline$ $\frac{160}{27}$

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