Solve frac{5^{4}*5^5*(-7)^4}{7^3*(-5)^11}

$$\frac { 5 ^ { 4 } \cdot 5 ^ { 5 } \cdot ( - 7 ) ^ { 4 } } { 7 ^ { 3 } \cdot ( - 5 ) ^ { 11 } }$$

Evaluate

$$-\frac{7}{25}=-0.28$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{5^{9}\left(-7\right)^{4}}{7^{3}\left(-5\right)^{11}}$$

Calculate 5 to the power of 9 and get 1953125.

$$\frac{1953125\left(-7\right)^{4}}{7^{3}\left(-5\right)^{11}}$$

Calculate -7 to the power of 4 and get 2401.

$$\frac{1953125\times 2401}{7^{3}\left(-5\right)^{11}}$$

Multiply 1953125 and 2401 to get 4689453125.

$$\frac{4689453125}{7^{3}\left(-5\right)^{11}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{4689453125}{343\left(-5\right)^{11}}$$

Calculate -5 to the power of 11 and get -48828125.

$$\frac{4689453125}{343\left(-48828125\right)}$$

Multiply 343 and -48828125 to get -16748046875.

$$\frac{4689453125}{-16748046875}$$

Reduce the fraction \frac{4689453125}{-16748046875} to lowest terms by extracting and canceling out 669921875.

$$-\frac{7}{25}$$

Factor

$$-\frac{7}{25} = -0.28$$