Solve [(3+4^{2}-5-3^3):7]^3:8^2+2^3

$$[ ( 3 + 4 ^ { 2 } - 5 - 3 ^ { 3 } ) : 7 ] ^ { 3 } : 8 ^ { 2 } + 2 ^ { 3 }$$

Evaluate

$$\frac{173419}{21952}\approx 7.899918003$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{\left(\frac{3+16-5-3^{3}}{7}\right)^{3}}{8^{2}}+2^{3}$$

Add 3 and 16 to get 19.

$$\frac{\left(\frac{19-5-3^{3}}{7}\right)^{3}}{8^{2}}+2^{3}$$

Subtract 5 from 19 to get 14.

$$\frac{\left(\frac{14-3^{3}}{7}\right)^{3}}{8^{2}}+2^{3}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{\left(\frac{14-27}{7}\right)^{3}}{8^{2}}+2^{3}$$

Subtract 27 from 14 to get -13.

$$\frac{\left(\frac{-13}{7}\right)^{3}}{8^{2}}+2^{3}$$

Fraction \frac{-13}{7} can be rewritten as -\frac{13}{7} by extracting the negative sign.

$$\frac{\left(-\frac{13}{7}\right)^{3}}{8^{2}}+2^{3}$$

Calculate -\frac{13}{7} to the power of 3 and get -\frac{2197}{343}.

$$\frac{-\frac{2197}{343}}{8^{2}}+2^{3}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{-\frac{2197}{343}}{64}+2^{3}$$

Express \frac{-\frac{2197}{343}}{64} as a single fraction.

$$\frac{-2197}{343\times 64}+2^{3}$$

Multiply 343 and 64 to get 21952.

$$\frac{-2197}{21952}+2^{3}$$

Fraction \frac{-2197}{21952} can be rewritten as -\frac{2197}{21952} by extracting the negative sign.

$$-\frac{2197}{21952}+2^{3}$$

Calculate 2 to the power of 3 and get 8.

$$-\frac{2197}{21952}+8$$

Add -\frac{2197}{21952} and 8 to get \frac{173419}{21952}.

$$\frac{173419}{21952}$$

Factor

$$\frac{37 \cdot 43 \cdot 109}{2 ^ {6} \cdot 7 ^ {3}} = 7\frac{19755}{21952} = 7.899918002915452$$