Solve (5^{4})^{6}:5^{21}-5^{2}-6^{2}]+30^{2}-{[6^2*7^2-(5+6*9)*2^2]-(31^2+3

$$( 5 ^ { 4 } ) ^ { 6 } : 5 ^ { 21 } - 5 ^ { 2 } - 6 ^ { 2 } ] + 30 ^ { 2 } - \{ [ 6 ^ { 2 } \times 7 ^ { 2 } - ( 5 + 6 \times 9 ) \times 2 ^ { 2 } ] - ( 31 ^ { 2 } + 3$$

Evaluate

$$64$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 6 to get 24.

$$\frac{5^{24}}{5^{21}}-5^{2}-6^{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 21 from 24 to get 3.

$$5^{3}-5^{2}-6^{2}$$

Calculate 5 to the power of 3 and get 125.

$$125-5^{2}-6^{2}$$

Calculate 5 to the power of 2 and get 25.

$$125-25-6^{2}$$

Subtract 25 from 125 to get 100.

$$100-6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$100-36$$

Subtract 36 from 100 to get 64.

$$64$$

Factor

$$2^{6}$$