Solve [(5^{2}*5^{3})^{4}:5^10]^4:(5^5)^8=

$$[ ( 5 ^ { 2 } \cdot 5 ^ { 3 } ) ^ { 4 } : 5 ^ { 10 } ] ^ { 4 } : ( 5 ^ { 5 } ) ^ { 8 } =$$

Evaluate

$$1$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\left(\frac{\left(5^{5}\right)^{4}}{5^{10}}\right)^{4}}{\left(5^{5}\right)^{8}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{\left(\frac{5^{20}}{5^{10}}\right)^{4}}{\left(5^{5}\right)^{8}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 20 to get 10.

$$\frac{\left(5^{10}\right)^{4}}{\left(5^{5}\right)^{8}}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 4 to get 40.

$$\frac{5^{40}}{\left(5^{5}\right)^{8}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 8 to get 40.

$$\frac{5^{40}}{5^{40}}$$

Divide 5^{40} by 5^{40} to get 1.

$$1$$

Factor

$$1$$