Solve (frac{(5^{4}*5^8)^3}{5^34})^2=

$$( \frac { ( 5 ^ { 4 } \cdot 5 ^ { 8 } ) ^ { 3 } } { 5 ^ { 34 } } ) ^ { 2 } =$$

Evaluate

$$625$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$\left(\frac{\left(5^{12}\right)^{3}}{5^{34}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 3 to get 36.

$$\left(\frac{5^{36}}{5^{34}}\right)^{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 34 from 36 to get 2.

$$\left(5^{2}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25^{2}$$

Calculate 25 to the power of 2 and get 625.

$$625$$

Factor

$$5^{4}$$