Solve frac{2*{4}^frac{5{2}}}{15}+frac{2*{4}^frac{7{2}}}{7}-13*4^4/96

$$\frac{ 2 \times { 4 }^{ \frac{ 5 }{ 2 } } }{ 15 } + \frac{ 2 \times { 4 }^{ \frac{ 7 }{ 2 } } }{ 7 } - \frac{ 13 \times { 4 }^{ 4 } }{ 96 }$$

Evaluate

$$\frac{216}{35}\approx 6.171428571$$

Solution Steps

Calculate 4 to the power of \frac{5}{2} and get 32.

$$\frac{2\times 32}{15}+\frac{2\times 4^{\frac{7}{2}}}{7}-\frac{13\times 4^{4}}{96}$$

Multiply 2 and 32 to get 64.

$$\frac{64}{15}+\frac{2\times 4^{\frac{7}{2}}}{7}-\frac{13\times 4^{4}}{96}$$

Calculate 4 to the power of \frac{7}{2} and get 128.

$$\frac{64}{15}+\frac{2\times 128}{7}-\frac{13\times 4^{4}}{96}$$

Multiply 2 and 128 to get 256.

$$\frac{64}{15}+\frac{256}{7}-\frac{13\times 4^{4}}{96}$$

Add \frac{64}{15} and \frac{256}{7} to get \frac{4288}{105}.

$$\frac{4288}{105}-\frac{13\times 4^{4}}{96}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{4288}{105}-\frac{13\times 256}{96}$$

Multiply 13 and 256 to get 3328.

$$\frac{4288}{105}-\frac{3328}{96}$$

Reduce the fraction \frac{3328}{96} to lowest terms by extracting and canceling out 32.

$$\frac{4288}{105}-\frac{104}{3}$$

Subtract \frac{104}{3} from \frac{4288}{105} to get \frac{216}{35}.

$$\frac{216}{35}$$

Factor

$$\frac{2 ^ {3} \cdot 3 ^ {3}}{5 \cdot 7} = 6\frac{6}{35} = 6.171428571428572$$