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What is the greatest whole number that is less than
((5)/(2))^(3)÷((3)/(4))^(2)?

What is the greatest whole number that is less than $\left(\frac{5}{2}\right)^{3} \div\left(\frac{3}{4}\right)^{2} ?$

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Evaluate rational exponents

Full solution

Q. What is the greatest whole number that is less than

\left(\frac{5}{2}\right)^{3} \div\left(\frac{3}{4}\right)^{2} ?

Calculate Power: Calculate $((5)/(2))^3$ . $\newline$ $((5)/(2))^3 = 125/8$
Calculate Square: Calculate $\left(\frac{3}{4}\right)^2$ . $\left(\frac{3}{4}\right)^2 = \frac{9}{16}$
Divide Results: Divide the results of the first two steps. $\newline$ $(125/8) \div (9/16) = (125/8) \times (16/9) = 250/9$
Find Whole Number: Find the greatest whole number less than $\frac{250}{9}$ . $\newline$ $\frac{250}{9} \approx 27.777...$ $\newline$ The greatest whole number less than $27.777...$ is $27$ .

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