Solve 6+3^{2}*5^{2}-2^{6}:2^4-11^5:11^3-9^2

$$6 + 3 ^ { 2 } \times 5 ^ { 2 } - 2 ^ { 6 } : 2 ^ { 4 } - 11 ^ { 5 } : 11 ^ { 3 } - 9 ^ { 2 }$$

Evaluate

$$25$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

$$6+3^{2}\times 5^{2}-2^{2}-\frac{11^{5}}{11^{3}}-9^{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 5 to get 2.

$$6+3^{2}\times 5^{2}-2^{2}-11^{2}-9^{2}$$

Calculate 3 to the power of 2 and get 9.

$$6+9\times 5^{2}-2^{2}-11^{2}-9^{2}$$

Calculate 5 to the power of 2 and get 25.

$$6+9\times 25-2^{2}-11^{2}-9^{2}$$

Multiply 9 and 25 to get 225.

$$6+225-2^{2}-11^{2}-9^{2}$$

Add 6 and 225 to get 231.

$$231-2^{2}-11^{2}-9^{2}$$

Calculate 2 to the power of 2 and get 4.

$$231-4-11^{2}-9^{2}$$

Subtract 4 from 231 to get 227.

$$227-11^{2}-9^{2}$$

Calculate 11 to the power of 2 and get 121.

$$227-121-9^{2}$$

Subtract 121 from 227 to get 106.

$$106-9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$106-81$$

Subtract 81 from 106 to get 25.

$$25$$

Factor

$$5^{2}$$