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Simplify the expression completely. root(3)(64)+root(3)(-8)-5root(3)(125)-root(3)(216) Answer:

Simplify the expression completely.\newline643+−83−51253−2163 \sqrt[3]{64}+\sqrt[3]{-8}-5 \sqrt[3]{125}-\sqrt[3]{216} \newlineAnswer:

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Q. Simplify the expression completely.\newline643+−83−51253−2163 \sqrt[3]{64}+\sqrt[3]{-8}-5 \sqrt[3]{125}-\sqrt[3]{216} \newlineAnswer:
  1. Simplify 6464 cube root: We will start by simplifying each cube root individually.\newline643\sqrt[3]{64} is the cube root of 6464, which is 44 because 43=644^3 = 64.
  2. Simplify −8-8 cube root: Next, −83\sqrt[3]{-8} is the cube root of −8-8, which is −2-2 because (−2)3=−8(-2)^3 = -8.
  3. Simplify 125125 cube root: Then, 1253\sqrt[3]{125} is the cube root of 125125, which is 55 because 53=1255^3 = 125.
  4. Multiply by 55: Now, 512535\sqrt[3]{125} is 55 times the cube root of 125125, which is 5×5=255\times5 = 25.
  5. Simplify 216216 cube root: After that, 2163\sqrt[3]{216} is the cube root of 216216, which is 66 because 63=2166^3 = 216.
  6. Combine simplified terms: Now we will combine all the simplified terms: 4+(−2)−25−64 + (-2) - 25 - 6
  7. Perform arithmetic operations: Perform the arithmetic operations: 4−2−25−6=2−25−6=−23−6=−294 - 2 - 25 - 6 = 2 - 25 - 6 = -23 - 6 = -29

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