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Select the answer which is equivalent to the given expression using your calculator. {:[(8a^(4))/((243 b)^((2)/(5)))],[a=6" and "b=32]:} 288 -288 864 -864

Select the answer which is equivalent to the given expression using your calculator.\newline8a4(243b)25a=6 and b=32 \begin{array}{c} \frac{8 a^{4}}{(243 b)^{\frac{2}{5}}} \\ a=6 \text { and } b=32 \end{array} \newline288288\newline−288 -288 \newline864864\newline−864 -864

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Full solution

Q. Select the answer which is equivalent to the given expression using your calculator.\newline8a4(243b)25a=6 and b=32 \begin{array}{c} \frac{8 a^{4}}{(243 b)^{\frac{2}{5}}} \\ a=6 \text { and } b=32 \end{array} \newline288288\newline−288 -288 \newline864864\newline−864 -864
  1. Substitute given values: First, let's substitute the given values of aa and bb into the expression.a=6a = 6 and b=32b = 32 So, the expression becomes (8⋅64)/((243⋅32)2/5)(8\cdot6^{4}) / ((243\cdot32)^{2/5}).
  2. Calculate 66 to the power of 44: Now, let's calculate 64=6×6×6×6=12966^4 = 6 \times 6 \times 6 \times 6 = 1296
  3. Multiply 88 by 12961296: Next, we multiply 88 by 12961296.\newline8×1296=103688 \times 1296 = 10368
  4. Calculate 243243 multiplied by 3232: Then, we calculate 243243 multiplied by 3232.\newline243×32=7776243 \times 32 = 7776
  5. Calculate (7776)2/5(7776)^{2/5}: Now, we need to calculate (7776)2/5(7776)^{2/5}. To do this, we can use a calculator. (7776)2/5≈144(7776)^{2/5} \approx 144
  6. Divide 1036810368 by 144144: Finally, we divide 1036810368 by 144144 to get the answer.\newline10368/144=7210368 / 144 = 72

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