Solve frac{5*(-4)^{15}*(-9)^{4}+4*3^{20}*(-8)^{4}}{-5*2^8*(-6)^19-7*2^29*(-27)^6}

$$\frac { 5 \cdot ( - 4 ) ^ { 15 } \cdot ( - 9 ) ^ { 4 } + 4 \cdot 3 ^ { 20 } \cdot ( - 8 ) ^ { 4 } } { - 5 \cdot 2 ^ { 8 } \cdot ( - 6 ) ^ { 19 } - 7 \cdot 2 ^ { 29 } \cdot ( - 27 ) ^ { 6 } }$$

Evaluate

$$-\frac{203761}{6288482304}\approx -0.000032402$$

Solution Steps

Calculate -4 to the power of 15 and get -1073741824.

$$\frac{5\left(-1073741824\right)\left(-9\right)^{4}+4\times 3^{20}\left(-8\right)^{4}}{-5\times 2^{8}\left(-6\right)^{19}-7\times 2^{29}\left(-27\right)^{6}}$$

Multiply 5 and -1073741824 to get -5368709120.

$$\frac{-5368709120\left(-9\right)^{4}+4\times 3^{20}\left(-8\right)^{4}}{-5\times 2^{8}\left(-6\right)^{19}-7\times 2^{29}\left(-27\right)^{6}}$$

Calculate -9 to the power of 4 and get 6561.

$$\frac{-5368709120\times 6561+4\times 3^{20}\left(-8\right)^{4}}{-5\times 2^{8}\left(-6\right)^{19}-7\times 2^{29}\left(-27\right)^{6}}$$

Multiply -5368709120 and 6561 to get -35224100536320.

$$\frac{-35224100536320+4\times 3^{20}\left(-8\right)^{4}}{-5\times 2^{8}\left(-6\right)^{19}-7\times 2^{29}\left(-27\right)^{6}}$$

Calculate 3 to the power of 20 and get 3486784401.

$$\frac{-35224100536320+4\times 3486784401\left(-8\right)^{4}}{-5\times 2^{8}\left(-6\right)^{19}-7\times 2^{29}\left(-27\right)^{6}}$$

Multiply 4 and 3486784401 to get 13947137604.

$$\frac{-35224100536320+13947137604\left(-8\right)^{4}}{-5\times 2^{8}\left(-6\right)^{19}-7\times 2^{29}\left(-27\right)^{6}}$$

Calculate -8 to the power of 4 and get 4096.

$$\frac{-35224100536320+13947137604\times 4096}{-5\times 2^{8}\left(-6\right)^{19}-7\times 2^{29}\left(-27\right)^{6}}$$

Multiply 13947137604 and 4096 to get 57127475625984.

$$\frac{-35224100536320+57127475625984}{-5\times 2^{8}\left(-6\right)^{19}-7\times 2^{29}\left(-27\right)^{6}}$$

Add -35224100536320 and 57127475625984 to get 21903375089664.

$$\frac{21903375089664}{-5\times 2^{8}\left(-6\right)^{19}-7\times 2^{29}\left(-27\right)^{6}}$$

Calculate 2 to the power of 8 and get 256.

$$\frac{21903375089664}{-5\times 256\left(-6\right)^{19}-7\times 2^{29}\left(-27\right)^{6}}$$

Multiply -5 and 256 to get -1280.

$$\frac{21903375089664}{-1280\left(-6\right)^{19}-7\times 2^{29}\left(-27\right)^{6}}$$

Calculate -6 to the power of 19 and get -609359740010496.

$$\frac{21903375089664}{-1280\left(-609359740010496\right)-7\times 2^{29}\left(-27\right)^{6}}$$

Multiply -1280 and -609359740010496 to get 779980467213434880.

$$\frac{21903375089664}{779980467213434880-7\times 2^{29}\left(-27\right)^{6}}$$

Calculate 2 to the power of 29 and get 536870912.

$$\frac{21903375089664}{779980467213434880-7\times 536870912\left(-27\right)^{6}}$$

Multiply 7 and 536870912 to get 3758096384.

$$\frac{21903375089664}{779980467213434880-3758096384\left(-27\right)^{6}}$$

Calculate -27 to the power of 6 and get 387420489.

$$\frac{21903375089664}{779980467213434880-3758096384\times 387420489}$$

Multiply 3758096384 and 387420489 to get 1455963538798411776.

$$\frac{21903375089664}{779980467213434880-1455963538798411776}$$

Subtract 1455963538798411776 from 779980467213434880 to get -675983071584976896.

$$\frac{21903375089664}{-675983071584976896}$$

Reduce the fraction \frac{21903375089664}{-675983071584976896} to lowest terms by extracting and canceling out 107495424.

$$-\frac{203761}{6288482304}$$

Factor

$$-\frac{203761}{6288482304} = -3.2402253858676042 \times 10^{-5}$$