Solve frac{(4*2)^{3}*(5^{2})^6*0^5}{2^2*4*5^10}

$$\frac { ( 4 \times 2 ) ^ { 3 } \times ( 5 ^ { 2 } ) ^ { 6 } \times 0 ^ { 5 } } { 2 ^ { 2 } \times 4 \times 5 ^ { 10 } }$$

Evaluate

$$0$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{\left(4\times 2\right)^{3}\times 5^{12}\times 0^{5}}{2^{2}\times 4\times 5^{10}}$$

Cancel out 5^{10} in both numerator and denominator.

$$\frac{0^{5}\times 5^{2}\times \left(2\times 4\right)^{3}}{4\times 2^{2}}$$

Calculate 0 to the power of 5 and get 0.

$$\frac{0\times 5^{2}\times \left(2\times 4\right)^{3}}{4\times 2^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{0\times 25\times \left(2\times 4\right)^{3}}{4\times 2^{2}}$$

Multiply 0 and 25 to get 0.

$$\frac{0\times \left(2\times 4\right)^{3}}{4\times 2^{2}}$$

Multiply 2 and 4 to get 8.

$$\frac{0\times 8^{3}}{4\times 2^{2}}$$

Calculate 8 to the power of 3 and get 512.

$$\frac{0\times 512}{4\times 2^{2}}$$

Multiply 0 and 512 to get 0.

$$\frac{0}{4\times 2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{0}{4\times 4}$$

Multiply 4 and 4 to get 16.

$$\frac{0}{16}$$

Zero divided by any non-zero number gives zero.

$$0$$

Factor

$$0$$