Solve (5^{4}*5^{2}*5)^{4}:5^{24}-5^{2}*3-(2^2)^4:(2^3)^2=

$$( 5 ^ { 4 } \cdot 5 ^ { 2 } \cdot 5 ) ^ { 4 } : 5 ^ { 24 } - 5 ^ { 2 } \cdot 3 - ( 2 ^ { 2 } ) ^ { 4 } : ( 2 ^ { 3 } ) ^ { 2 } =$$

Evaluate

$$546$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\left(5^{6}\times 5\right)^{4}}{5^{24}}-5^{2}\times 3-\frac{\left(2^{2}\right)^{4}}{\left(2^{3}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{\left(5^{7}\right)^{4}}{5^{24}}-5^{2}\times 3-\frac{\left(2^{2}\right)^{4}}{\left(2^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$\frac{5^{28}}{5^{24}}-5^{2}\times 3-\frac{\left(2^{2}\right)^{4}}{\left(2^{3}\right)^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 24 from 28 to get 4.

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

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

$$5^{4}-5^{2}\times 3-\frac{2^{8}}{\left(2^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$5^{4}-5^{2}\times 3-\frac{2^{8}}{2^{6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 8 to get 2.

$$5^{4}-5^{2}\times 3-2^{2}$$

Calculate 5 to the power of 4 and get 625.

$$625-5^{2}\times 3-2^{2}$$

Calculate 5 to the power of 2 and get 25.

$$625-25\times 3-2^{2}$$

Multiply 25 and 3 to get 75.

$$625-75-2^{2}$$

Subtract 75 from 625 to get 550.

$$550-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$550-4$$

Subtract 4 from 550 to get 546.

$$546$$

Factor

$$2\times 3\times 7\times 13$$