Solve -3^5*2^4*8/-2^7*9^12*18

$$\frac{ { -3 }^{ 5 } \times { 2 }^{ 4 } \times 8 }{ - { 2 }^{ 7 } \times { 9 }^{ 12 } \times 18 }$$

Evaluate

$$\frac{1}{20920706406}\approx 4.779953318 \cdot 10^{-11}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{4\left(-3\right)^{5}\times 2^{4}}{9\left(-2^{7}\right)\times 9^{12}}$$

Calculate -3 to the power of 5 and get -243.

$$\frac{4\left(-243\right)\times 2^{4}}{9\left(-2^{7}\right)\times 9^{12}}$$

Multiply 4 and -243 to get -972.

$$\frac{-972\times 2^{4}}{9\left(-2^{7}\right)\times 9^{12}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{-972\times 16}{9\left(-2^{7}\right)\times 9^{12}}$$

Multiply -972 and 16 to get -15552.

$$\frac{-15552}{9\left(-2^{7}\right)\times 9^{12}}$$

To multiply powers of the same base, add their exponents. Add 1 and 12 to get 13.

$$\frac{-15552}{9^{13}\left(-2^{7}\right)}$$

Calculate 9 to the power of 13 and get 2541865828329.

$$\frac{-15552}{2541865828329\left(-2^{7}\right)}$$

Calculate 2 to the power of 7 and get 128.

$$\frac{-15552}{2541865828329\left(-128\right)}$$

Multiply 2541865828329 and -128 to get -325358826026112.

$$\frac{-15552}{-325358826026112}$$

Reduce the fraction \frac{-15552}{-325358826026112} to lowest terms by extracting and canceling out -15552.

$$\frac{1}{20920706406}$$

Factor

$$\frac{1}{2 \cdot 3 ^ {21}} = 4.7799533179874025 \times 10^{-11}$$