Solve (1^{3}+2^3+3^3+4^3)^-frac{7{2}}

$$( 1 ^ { 3 } + 2 ^ { 3 } + 3 ^ { 3 } + 4 ^ { 3 } ) ^ { - \frac { 7 } { 2 } }$$

Evaluate

$$\frac{1}{10000000}=0.0000001$$

Solution Steps

Calculate 1 to the power of 3 and get 1.

$$\left(1+2^{3}+3^{3}+4^{3}\right)^{-\frac{7}{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\left(1+8+3^{3}+4^{3}\right)^{-\frac{7}{2}}$$

Add 1 and 8 to get 9.

$$\left(9+3^{3}+4^{3}\right)^{-\frac{7}{2}}$$

Calculate 3 to the power of 3 and get 27.

$$\left(9+27+4^{3}\right)^{-\frac{7}{2}}$$

Add 9 and 27 to get 36.

$$\left(36+4^{3}\right)^{-\frac{7}{2}}$$

Calculate 4 to the power of 3 and get 64.

$$\left(36+64\right)^{-\frac{7}{2}}$$

Add 36 and 64 to get 100.

$$100^{-\frac{7}{2}}$$

Calculate 100 to the power of -\frac{7}{2} and get \frac{1}{10000000}.

$$\frac{1}{10000000}$$

Factor

$$\frac{1}{2 ^ {7} \cdot 5 ^ {7}} = 1 \times 10^{-7}$$