Solve 8*7/15*(25-9*(7/15)^2)^-frac{1{2}}

$$8 \times \frac { 7 } { 15 } \times ( 25 - 9 \times ( \frac { 7 } { 15 } ) ^ { 2 } ) ^ { - \frac { 1 } { 2 } }$$

Evaluate

$$\frac{7}{9}\approx 0.777777778$$

Solution Steps

Multiply 8 and \frac{7}{15} to get \frac{56}{15}.

$$\frac{56}{15}\left(25-9\times \left(\frac{7}{15}\right)^{2}\right)^{-\frac{1}{2}}$$

Calculate \frac{7}{15} to the power of 2 and get \frac{49}{225}.

$$\frac{56}{15}\left(25-9\times \frac{49}{225}\right)^{-\frac{1}{2}}$$

Multiply 9 and \frac{49}{225} to get \frac{49}{25}.

$$\frac{56}{15}\left(25-\frac{49}{25}\right)^{-\frac{1}{2}}$$

Subtract \frac{49}{25} from 25 to get \frac{576}{25}.

$$\frac{56}{15}\times \left(\frac{576}{25}\right)^{-\frac{1}{2}}$$

Calculate \frac{576}{25} to the power of -\frac{1}{2} and get \frac{5}{24}.

$$\frac{56}{15}\times \frac{5}{24}$$

Multiply \frac{56}{15} and \frac{5}{24} to get \frac{7}{9}.

$$\frac{7}{9}$$

Factor

$$\frac{7}{3 ^ {2}} = 0.7777777777777778$$