Select the answer which is equivalent to the given expression using your calculator. (-9a^(4))/((243 b)^((2)/(5))) a=-6 and b=1024 -81 81 3 -3

Question

Select the answer which is equivalent to the given expression using your calculator.  (-9a^(4))/((243 b)^((2)/(5)))  a=-6 and  b=1024  -81 81 3  -3

Bytelearn · Accepted Answer

Substitute Given Values: First, let's substitute the given values of a and b into the expression. a = -6 b = 1024 The expression becomes (-9*(-6)^(4))/((243*1024)^((2)/(5))).Calculate (-6)^(4): Now, calculate the value of (-6)^(4). Since -6 is raised to an even power, the result will be positive. (-6)^(4) = (-6)*(-6)*(-6)*(-6) = 1296.Calculate Numerator: Next, calculate the numerator by multiplying -9 by 1296. -9 * 1296 = -11664.Calculate Denominator: Now, let's focus on the denominator. We need to calculate (243*1024)^((2)/(5)). First, multiply 243 by 1024. 243 * 1024 = 248832.Calculate (243*1024)^((2)/(5)): Next, we need to take the fifth root of 248832 squared. This is equivalent to raising 248832 to the power of 2/5. (248832)^(2/5) can be calculated using a calculator.Divide Numerator by Denominator: Using a calculator, we find that (248832)^(2/5) is approximately 81.998, which is very close to 82. Since we are looking for an equivalent expression and the options are integers, we can round this to 82 for the purpose of this problem.Now, divide the numerator by the denominator. -11664 / 82 = -142.24. This does not match any of the answer choices, which suggests there might be a mistake. Let's recheck our calculations.

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\frac{-9 a^{4}}{(243 b)^{\frac{2}{5}}}$ $\newline$ $a=-6$ and $b=1024$ $\newline$ $-81$ $\newline$ $81$ $\newline$ $3$ $\newline$ $-3$

Full solution

More problems from Operations with rational exponents

Related topics

Select the answer which is equivalent to the given expression using your calculator.\newline−9a4(243b)25 \frac{-9 a^{4}}{(243 b)^{\frac{2}{5}}} (243b)52​−9a4​\newlinea=−6 a=-6 a=−6 and b=1024 b=1024 b=1024\newline−81 -81 −81\newline818181\newline333\newline−3 -3 −3

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\frac{-9 a^{4}}{(243 b)^{\frac{2}{5}}}$ $\newline$ $a=-6$ and $b=1024$ $\newline$ $-81$ $\newline$ $81$ $\newline$ $3$ $\newline$ $-3$