Solve -8/32^2+1/52^5+16(2)

$$- \frac{ 8 }{ 3 } { 2 }^{ 2 } + \frac{ 1 }{ 5 } { 2 }^{ 5 } +16(2)$$

Evaluate

$$\frac{416}{15}\approx 27.733333333$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$-\frac{8}{3}\times 4+\frac{1}{5}\times 2^{5}+16\times 2$$

Express -\frac{8}{3}\times 4 as a single fraction.

$$\frac{-8\times 4}{3}+\frac{1}{5}\times 2^{5}+16\times 2$$

Multiply -8 and 4 to get -32.

$$\frac{-32}{3}+\frac{1}{5}\times 2^{5}+16\times 2$$

Fraction \frac{-32}{3} can be rewritten as -\frac{32}{3} by extracting the negative sign.

$$-\frac{32}{3}+\frac{1}{5}\times 2^{5}+16\times 2$$

Calculate 2 to the power of 5 and get 32.

$$-\frac{32}{3}+\frac{1}{5}\times 32+16\times 2$$

Multiply \frac{1}{5} and 32 to get \frac{32}{5}.

$$-\frac{32}{3}+\frac{32}{5}+16\times 2$$

Least common multiple of 3 and 5 is 15. Convert -\frac{32}{3} and \frac{32}{5} to fractions with denominator 15.

$$-\frac{160}{15}+\frac{96}{15}+16\times 2$$

Since -\frac{160}{15} and \frac{96}{15} have the same denominator, add them by adding their numerators.

$$\frac{-160+96}{15}+16\times 2$$

Add -160 and 96 to get -64.

$$-\frac{64}{15}+16\times 2$$

Multiply 16 and 2 to get 32.

$$-\frac{64}{15}+32$$

Convert 32 to fraction \frac{480}{15}.

$$-\frac{64}{15}+\frac{480}{15}$$

Since -\frac{64}{15} and \frac{480}{15} have the same denominator, add them by adding their numerators.

$$\frac{-64+480}{15}$$

Add -64 and 480 to get 416.

$$\frac{416}{15}$$

Factor

$$\frac{2 ^ {5} \cdot 13}{3 \cdot 5} = 27\frac{11}{15} = 27.733333333333334$$