Question

(5^(4/7)*11^(2/3))^21/55^12

Answer 1

$\frac{(5^{ \frac{4}{7} }*11^{ \frac{2}{3} })^{21}}{55^{12}} = \frac{5^{4*21:7}*11^{2*21:3}}{55^{12}}$ $= \frac{5^{12}*11^{14}}{5^{12}*11^{12}} =11^2=121$

Answer 2

To simplify the expression (5^(4/7) * 11^(2/3))^(21/55) / 5^12, let's break it down step by step.

Step 1: Simplify the exponent expressions inside the parentheses.

5^(4/7) = ∛(5^4) = ∛625 = 5

11^(2/3) = ∛(11^2) = ∛121 = 11

Now the expression becomes (5 * 11)^(21/55) / 5^12.

Step 2: Simplify the numerator.

(5 * 11)^(21/55) = 55^(21/55)

Step 3: Simplify the denominator.

5^12 = 5^(12/1) = 5^12

Now the expression becomes 55^(21/55) / 5^12.

Step 4: Simplify the exponent expression in the numerator.

55^(21/55) = ∛(55^21) = ∛(94143178827) ≈ 337.028

Finally, the simplified expression is approximately 337.028 / 5^12.