Solve {left(frac{5^7*-5/-5^12right)}^10}{left(-5^2right)^4}-{-5}^2

$$\frac{ { \left( \frac{ { 5 }^{ 7 } \times -5 }{ { -5 }^{ 12 } } \right) }^{ 10 } }{ { \left( { -5 }^{ 2 } \right) }^{ 4 } } - { -5 }^{ 2 }$$

Evaluate

$$-\frac{88817841970012523233890533447265624}{3552713678800500929355621337890625}\approx -25$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{\left(\frac{5^{7}\left(-5\right)}{\left(-5\right)^{12}}\right)^{10}}{\left(-5\right)^{8}}-\left(-5\right)^{2}$$

Cancel out -5 in both numerator and denominator.

$$\frac{\left(\frac{5^{7}}{\left(-5\right)^{11}}\right)^{10}}{\left(-5\right)^{8}}-\left(-5\right)^{2}$$

Calculate 5 to the power of 7 and get 78125.

$$\frac{\left(\frac{78125}{\left(-5\right)^{11}}\right)^{10}}{\left(-5\right)^{8}}-\left(-5\right)^{2}$$

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

$$\frac{\left(\frac{78125}{-48828125}\right)^{10}}{\left(-5\right)^{8}}-\left(-5\right)^{2}$$

Reduce the fraction \frac{78125}{-48828125} to lowest terms by extracting and canceling out 78125.

$$\frac{\left(-\frac{1}{625}\right)^{10}}{\left(-5\right)^{8}}-\left(-5\right)^{2}$$

Calculate -\frac{1}{625} to the power of 10 and get \frac{1}{9094947017729282379150390625}.

$$\frac{\frac{1}{9094947017729282379150390625}}{\left(-5\right)^{8}}-\left(-5\right)^{2}$$

Calculate -5 to the power of 8 and get 390625.

$$\frac{\frac{1}{9094947017729282379150390625}}{390625}-\left(-5\right)^{2}$$

Express \frac{\frac{1}{9094947017729282379150390625}}{390625} as a single fraction.

$$\frac{1}{9094947017729282379150390625\times 390625}-\left(-5\right)^{2}$$

Multiply 9094947017729282379150390625 and 390625 to get 3552713678800500929355621337890625.

$$\frac{1}{3552713678800500929355621337890625}-\left(-5\right)^{2}$$

Calculate -5 to the power of 2 and get 25.

$$\frac{1}{3552713678800500929355621337890625}-25$$

Subtract 25 from \frac{1}{3552713678800500929355621337890625} to get -\frac{88817841970012523233890533447265624}{3552713678800500929355621337890625}.

$$-\frac{88817841970012523233890533447265624}{3552713678800500929355621337890625}$$

Factor

$$-\frac{88817841970012523233890533447265624}{3552713678800500929355621337890625} = -25\frac{2.8823037615171176 \times 10^{18}}{3.5527136788005014 \times 10^{33}} = -25$$