Question

Find the relation between $2^9{\left(\frac{5}{4}\right)}^4$ and $3^4{\left(\frac{5}{3}\right)}^4$

• A. $29{\left(\frac{5}{4}\right)}^4\ge 3^4{\left(\frac{5}{3}\right)}^4$
• B. $3^4{\left(\frac{5}{3}\right)}^4>2^9{\left(\frac{5}{4}\right)}^4$
• C. $Bothareequal$
• D. $3^4{\left(\frac{5}{3}\right)}^4<2^9{\left(\frac{5}{4}\right)}^4$

Answer 1

The correct option is B $3^4{\left(\frac{5}{3}\right)}^4>2^9{\left(\frac{5}{4}\right)}^4$

$2^9{\left(\frac{5}{4}\right)}^4=2\times 5^4$
$3^4{\left(\frac{5}{3}\right)}^4=3\times 5^4$
So, $3^4{\left(\frac{5}{3}\right)}^4$ is greater.