Solve [(7^{7}:7^{5}-3^{2}*3+2^{4})-(6^2+2^2*3-5^8:5^6)]*15

$$[ ( 7 ^ { 7 } : 7 ^ { 5 } - 3 ^ { 2 } \cdot 3 + 2 ^ { 4 } ) - ( 6 ^ { 2 } + 2 ^ { 2 } \cdot 3 - 5 ^ { 8 } : 5 ^ { 6 } ) ] \cdot 15$$

Evaluate

$$225$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 7 to get 2.

$$\left(7^{2}-3^{2}\times 3+2^{4}-\left(6^{2}+2^{2}\times 3-\frac{5^{8}}{5^{6}}\right)\right)\times 15$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\left(7^{2}-3^{3}+2^{4}-\left(6^{2}+2^{2}\times 3-\frac{5^{8}}{5^{6}}\right)\right)\times 15$$

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

$$\left(7^{2}-3^{3}+2^{4}-\left(6^{2}+2^{2}\times 3-5^{2}\right)\right)\times 15$$

Calculate 7 to the power of 2 and get 49.

$$\left(49-3^{3}+2^{4}-\left(6^{2}+2^{2}\times 3-5^{2}\right)\right)\times 15$$

Calculate 3 to the power of 3 and get 27.

$$\left(49-27+2^{4}-\left(6^{2}+2^{2}\times 3-5^{2}\right)\right)\times 15$$

Subtract 27 from 49 to get 22.

$$\left(22+2^{4}-\left(6^{2}+2^{2}\times 3-5^{2}\right)\right)\times 15$$

Calculate 2 to the power of 4 and get 16.

$$\left(22+16-\left(6^{2}+2^{2}\times 3-5^{2}\right)\right)\times 15$$

Add 22 and 16 to get 38.

$$\left(38-\left(6^{2}+2^{2}\times 3-5^{2}\right)\right)\times 15$$

Calculate 6 to the power of 2 and get 36.

$$\left(38-\left(36+2^{2}\times 3-5^{2}\right)\right)\times 15$$

Calculate 2 to the power of 2 and get 4.

$$\left(38-\left(36+4\times 3-5^{2}\right)\right)\times 15$$

Multiply 4 and 3 to get 12.

$$\left(38-\left(36+12-5^{2}\right)\right)\times 15$$

Add 36 and 12 to get 48.

$$\left(38-\left(48-5^{2}\right)\right)\times 15$$

Calculate 5 to the power of 2 and get 25.

$$\left(38-\left(48-25\right)\right)\times 15$$

Subtract 25 from 48 to get 23.

$$\left(38-23\right)\times 15$$

Subtract 23 from 38 to get 15.

$$15\times 15$$

Multiply 15 and 15 to get 225.

$$225$$

Factor

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