Solve (-24+21):3^4+36:(-3^2)-4^2*2^15-sqrt{-32}

$$( - 24 + 21 ) : 3 ^ { 4 } + 36 : ( - 3 ^ { 2 } ) - 4 ^ { 2 } \cdot 2 ^ { 15 } - \sqrt { - 32 }$$

Evaluate (complex solution)

$$-4\sqrt{2}i-\frac{14155885}{27}\approx -524292.037037037-5.656854249i$$

Solution Steps

Add -24 and 21 to get -3.

$$\frac{-3}{3^{4}}+\frac{36}{-3^{2}}-4^{2}\times 2^{15}-\sqrt{-32}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{-3}{81}+\frac{36}{-3^{2}}-4^{2}\times 2^{15}-\sqrt{-32}$$

Reduce the fraction \frac{-3}{81} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{27}+\frac{36}{-3^{2}}-4^{2}\times 2^{15}-\sqrt{-32}$$

Calculate 3 to the power of 2 and get 9.

$$-\frac{1}{27}+\frac{36}{-9}-4^{2}\times 2^{15}-\sqrt{-32}$$

Divide 36 by -9 to get -4.

$$-\frac{1}{27}-4-4^{2}\times 2^{15}-\sqrt{-32}$$

Convert 4 to fraction \frac{108}{27}.

$$-\frac{1}{27}-\frac{108}{27}-4^{2}\times 2^{15}-\sqrt{-32}$$

Since -\frac{1}{27} and \frac{108}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-108}{27}-4^{2}\times 2^{15}-\sqrt{-32}$$

Subtract 108 from -1 to get -109.

$$-\frac{109}{27}-4^{2}\times 2^{15}-\sqrt{-32}$$

Calculate 4 to the power of 2 and get 16.

$$-\frac{109}{27}-16\times 2^{15}-\sqrt{-32}$$

Calculate 2 to the power of 15 and get 32768.

$$-\frac{109}{27}-16\times 32768-\sqrt{-32}$$

Multiply 16 and 32768 to get 524288.

$$-\frac{109}{27}-524288-\sqrt{-32}$$

Convert 524288 to fraction \frac{14155776}{27}.

$$-\frac{109}{27}-\frac{14155776}{27}-\sqrt{-32}$$

Since -\frac{109}{27} and \frac{14155776}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-109-14155776}{27}-\sqrt{-32}$$

Subtract 14155776 from -109 to get -14155885.

$$-\frac{14155885}{27}-\sqrt{-32}$$

Factor -32=\left(4i\right)^{2}\times 2. Rewrite the square root of the product \sqrt{\left(4i\right)^{2}\times 2} as the product of square roots \sqrt{\left(4i\right)^{2}}\sqrt{2}. Take the square root of \left(4i\right)^{2}.

$$-\frac{14155885}{27}-4i\sqrt{2}$$

Factor (complex solution)

$$-2^{\frac{5}{2}}i-\frac{14155885}{27}$$

Evaluate

$$\text{Indeterminate}$$