Solve 8^{4}div8^{4}*8^{0}*7^{5}div7^2*7^-3*5^3div5^1

$$8 ^ { 4 } \div 8 ^ { 4 } \times 8 ^ { 0 } \times 7 ^ { 5 } \div 7 ^ { 2 } \times 7 ^ { - 3 } \times 5 ^ { 3 } \div 5 ^ { 1 }$$

Evaluate

$$25$$

Solution Steps

Divide 8^{4} by 8^{4} to get 1.

$$\frac{\frac{1\times 8^{0}\times 7^{5}}{7^{2}}\times 7^{-3}\times 5^{3}}{5^{1}}$$

Cancel out 7^{2} in both numerator and denominator.

$$\frac{7^{3}\times 8^{0}\times 7^{-3}\times 5^{3}}{5^{1}}$$

Calculate 8 to the power of 0 and get 1.

$$\frac{7^{3}\times 1\times 7^{-3}\times 5^{3}}{5^{1}}$$

Calculate 7 to the power of -3 and get \frac{1}{343}.

$$\frac{7^{3}\times 1\times \frac{1}{343}\times 5^{3}}{5^{1}}$$

Multiply 1 and \frac{1}{343} to get \frac{1}{343}.

$$\frac{7^{3}\times \frac{1}{343}\times 5^{3}}{5^{1}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{7^{3}\times \frac{1}{343}\times 125}{5^{1}}$$

Multiply \frac{1}{343} and 125 to get \frac{125}{343}.

$$\frac{7^{3}\times \frac{125}{343}}{5^{1}}$$

Calculate 5 to the power of 1 and get 5.

$$\frac{7^{3}\times \frac{125}{343}}{5}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{343\times \frac{125}{343}}{5}$$

Multiply 343 and \frac{125}{343} to get 125.

$$\frac{125}{5}$$

Divide 125 by 5 to get 25.

$$25$$

Factor

$$5^{2}$$