Solve (14^{2}:7^{2}+5^{5}:5^{3})*2^{2}+{[3^{2}*5-(12*2^{2}-6):7]+3^2}^2:4^2-14^2

$$( 14 ^ { 2 } : 7 ^ { 2 } + 5 ^ { 5 } : 5 ^ { 3 } ) \times 2 ^ { 2 } + \{ [ 3 ^ { 2 } \times 5 - ( 12 \times 2 ^ { 2 } - 6 ) : 7 ] + 3 ^ { 2 } \} ^ { 2 } : 4 ^ { 2 } - 14 ^ { 2 }$$

Evaluate

$$64$$

Solution Steps

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

$$\left(\frac{14^{2}}{7^{2}}+5^{2}\right)\times 2^{2}+\frac{\left(3^{2}\times 5-\frac{12\times 2^{2}-6}{7}+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Calculate 14 to the power of 2 and get 196.

$$\left(\frac{196}{7^{2}}+5^{2}\right)\times 2^{2}+\frac{\left(3^{2}\times 5-\frac{12\times 2^{2}-6}{7}+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Calculate 7 to the power of 2 and get 49.

$$\left(\frac{196}{49}+5^{2}\right)\times 2^{2}+\frac{\left(3^{2}\times 5-\frac{12\times 2^{2}-6}{7}+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Divide 196 by 49 to get 4.

$$\left(4+5^{2}\right)\times 2^{2}+\frac{\left(3^{2}\times 5-\frac{12\times 2^{2}-6}{7}+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\left(4+25\right)\times 2^{2}+\frac{\left(3^{2}\times 5-\frac{12\times 2^{2}-6}{7}+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Add 4 and 25 to get 29.

$$29\times 2^{2}+\frac{\left(3^{2}\times 5-\frac{12\times 2^{2}-6}{7}+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Calculate 2 to the power of 2 and get 4.

$$29\times 4+\frac{\left(3^{2}\times 5-\frac{12\times 2^{2}-6}{7}+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Multiply 29 and 4 to get 116.

$$116+\frac{\left(3^{2}\times 5-\frac{12\times 2^{2}-6}{7}+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Calculate 3 to the power of 2 and get 9.

$$116+\frac{\left(9\times 5-\frac{12\times 2^{2}-6}{7}+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Multiply 9 and 5 to get 45.

$$116+\frac{\left(45-\frac{12\times 2^{2}-6}{7}+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Calculate 2 to the power of 2 and get 4.

$$116+\frac{\left(45-\frac{12\times 4-6}{7}+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Multiply 12 and 4 to get 48.

$$116+\frac{\left(45-\frac{48-6}{7}+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Subtract 6 from 48 to get 42.

$$116+\frac{\left(45-\frac{42}{7}+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Divide 42 by 7 to get 6.

$$116+\frac{\left(45-6+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Subtract 6 from 45 to get 39.

$$116+\frac{\left(39+3^{2}\right)^{2}}{4^{2}}-14^{2}$$

Calculate 3 to the power of 2 and get 9.

$$116+\frac{\left(39+9\right)^{2}}{4^{2}}-14^{2}$$

Add 39 and 9 to get 48.

$$116+\frac{48^{2}}{4^{2}}-14^{2}$$

Calculate 48 to the power of 2 and get 2304.

$$116+\frac{2304}{4^{2}}-14^{2}$$

Calculate 4 to the power of 2 and get 16.

$$116+\frac{2304}{16}-14^{2}$$

Divide 2304 by 16 to get 144.

$$116+144-14^{2}$$

Add 116 and 144 to get 260.

$$260-14^{2}$$

Calculate 14 to the power of 2 and get 196.

$$260-196$$

Subtract 196 from 260 to get 64.

$$64$$

Factor

$$2^{6}$$