Solve frac{6^-5*-2^-6*6^2*6^3*{-2}^5}{{left({-2}^4*{6}^2right)}^-2}

$$\frac{ { 6 }^{ -5 } \times { -2 }^{ -6 } \times { 6 }^{ 2 } \times { 6 }^{ 3 } \times { -2 }^{ 5 } }{ { \left( { -2 }^{ 4 } \times { 6 }^{ 2 } \right) }^{ -2 } }$$

Evaluate

$$-165888$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -5 and 2 to get -3.

$$\frac{6^{-3}\left(-2\right)^{-6}\times 6^{3}\left(-2\right)^{5}}{\left(\left(-2\right)^{4}\times 6^{2}\right)^{-2}}$$

Multiply 6^{-3} and 6^{3} to get 1.

$$\frac{\left(-2\right)^{-6}\left(-2\right)^{5}}{\left(\left(-2\right)^{4}\times 6^{2}\right)^{-2}}$$

To multiply powers of the same base, add their exponents. Add -6 and 5 to get -1.

$$\frac{\left(-2\right)^{-1}}{\left(\left(-2\right)^{4}\times 6^{2}\right)^{-2}}$$

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

$$\frac{-\frac{1}{2}}{\left(\left(-2\right)^{4}\times 6^{2}\right)^{-2}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{-\frac{1}{2}}{\left(16\times 6^{2}\right)^{-2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{-\frac{1}{2}}{\left(16\times 36\right)^{-2}}$$

Multiply 16 and 36 to get 576.

$$\frac{-\frac{1}{2}}{576^{-2}}$$

Calculate 576 to the power of -2 and get \frac{1}{331776}.

$$\frac{-\frac{1}{2}}{\frac{1}{331776}}$$

Divide -\frac{1}{2} by \frac{1}{331776} by multiplying -\frac{1}{2} by the reciprocal of \frac{1}{331776}.

$$-\frac{1}{2}\times 331776$$

Multiply -\frac{1}{2} and 331776 to get -165888.

$$-165888$$

Factor

$$-165888$$