Solve 3^{2}*3^{3}-5*[2*5^{2}-7^{5}:(7^{5}:7^{2})]^5-11^3:(11^6:11^5)

$$3 ^ { 2 } \times 3 ^ { 3 } - 5 \times [ 2 \times 5 ^ { 2 } - 7 ^ { 5 } : ( 7 ^ { 5 } : 7 ^ { 2 } ) ] ^ { 5 } - 11 ^ { 3 } : ( 11 ^ { 6 } : 11 ^ { 5 } )$$

Evaluate

$$117$$

Solution Steps

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

$$3^{5}-5\left(2\times 5^{2}-\frac{7^{5}}{\frac{7^{5}}{7^{2}}}\right)^{5}-\frac{11^{3}}{\frac{11^{6}}{11^{5}}}$$

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

$$3^{5}-5\left(2\times 5^{2}-\frac{7^{5}}{7^{3}}\right)^{5}-\frac{11^{3}}{\frac{11^{6}}{11^{5}}}$$

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

$$3^{5}-5\left(2\times 5^{2}-7^{2}\right)^{5}-\frac{11^{3}}{\frac{11^{6}}{11^{5}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 6 to get 1.

$$3^{5}-5\left(2\times 5^{2}-7^{2}\right)^{5}-\frac{11^{3}}{11^{1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

$$3^{5}-5\left(2\times 5^{2}-7^{2}\right)^{5}-11^{2}$$

Calculate 3 to the power of 5 and get 243.

$$243-5\left(2\times 5^{2}-7^{2}\right)^{5}-11^{2}$$

Calculate 5 to the power of 2 and get 25.

$$243-5\left(2\times 25-7^{2}\right)^{5}-11^{2}$$

Multiply 2 and 25 to get 50.

$$243-5\left(50-7^{2}\right)^{5}-11^{2}$$

Calculate 7 to the power of 2 and get 49.

$$243-5\left(50-49\right)^{5}-11^{2}$$

Subtract 49 from 50 to get 1.

$$243-5\times 1^{5}-11^{2}$$

Calculate 1 to the power of 5 and get 1.

$$243-5\times 1-11^{2}$$

Multiply 5 and 1 to get 5.

$$243-5-11^{2}$$

Subtract 5 from 243 to get 238.

$$238-11^{2}$$

Calculate 11 to the power of 2 and get 121.

$$238-121$$

Subtract 121 from 238 to get 117.

$$117$$

Factor

$$3^{2}\times 13$$