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(ii) Write the value of (root(3)(27))/(9^(2)) as a fraction in its LOWEST terms.

(ii) Write the value of 27392 \frac{\sqrt[3]{27}}{9^{2}} as a fraction in its LOWEST terms.

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Full solution

Q. (ii) Write the value of 27392 \frac{\sqrt[3]{27}}{9^{2}} as a fraction in its LOWEST terms.
  1. Evaluate Cube Root of 2727: Evaluate the cube root of 2727.\newlineThe cube root of 2727 is the number that, when multiplied by itself three times, gives 2727.\newline273=3\sqrt[3]{27} = 3 because 3×3×3=273 \times 3 \times 3 = 27.
  2. Evaluate 99 Squared: Evaluate 99 squared.\newline99 squared (929^2) is 99 multiplied by itself.\newline92=9×9=819^2 = 9 \times 9 = 81.
  3. Divide Cube Root by 99 Squared: Divide the cube root of 2727 by 99 squared.\newlineNow we divide the result from Step 11 by the result from Step 22.\newline27392=381\frac{\sqrt[3]{27}}{9^2} = \frac{3}{81}.
  4. Simplify the Fraction: Simplify the fraction.\newlineTo simplify the fraction 381\frac{3}{81}, we find the greatest common divisor (GCD) of 33 and 8181, which is 33.\newlineDivide both the numerator and the denominator by the GCD to simplify the fraction.\newline381=(3/3)(81/3)=127\frac{3}{81} = \frac{(3/3)}{(81/3)} = \frac{1}{27}.

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