Evaluate (3/4)^1.5*(2/3)^2.5

${(\frac{3}{4})}^{1.5} \cdot {(\frac{2}{3})}^{2.5}$

Step 1

Apply the product rule to $\frac{3}{4}$ .

$\frac{3^{1.5}}{4^{1.5}} \cdot {(\frac{2}{3})}^{2.5}$

Step 2

Raise $3$ to the power of $1.5$ .

$\frac{5.19615242}{4^{1.5}} \cdot {(\frac{2}{3})}^{2.5}$

Step 3

Raise $4$ to the power of $1.5$ .

$\frac{5.19615242}{8} \cdot {(\frac{2}{3})}^{2.5}$

Step 4

Divide $5.19615242$ by $8$ .

$0.64951905 \cdot {(\frac{2}{3})}^{2.5}$

Step 5

Apply the product rule to $\frac{2}{3}$ .

$0.64951905 \cdot \frac{2^{2.5}}{3^{2.5}}$

Step 6

Raise $2$ to the power of $2.5$ .

$0.64951905 \cdot \frac{5.65685424}{3^{2.5}}$

Step 7

Raise $3$ to the power of $2.5$ .

$0.64951905 \cdot \frac{5.65685424}{15.58845726}$

Step 8

Divide $5.65685424$ by $15.58845726$ .

$0.64951905 \cdot 0.36288736$

Step 9

Multiply $0.64951905$ by $0.36288736$ .

$0.23570226$