Solve (5^{4}:5^{3}+7^2-10):4+(4*3+3^2-4^2)^2=

$$( 5 ^ { 4 } : 5 ^ { 3 } + 7 ^ { 2 } - 10 ) : 4 + ( 4 \cdot 3 + 3 ^ { 2 } - 4 ^ { 2 } ) ^ { 2 } =$$

Evaluate

$$36$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 4 to get 1.

$$\frac{5^{1}+7^{2}-10}{4}+\left(4\times 3+3^{2}-4^{2}\right)^{2}$$

Calculate 5 to the power of 1 and get 5.

$$\frac{5+7^{2}-10}{4}+\left(4\times 3+3^{2}-4^{2}\right)^{2}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{5+49-10}{4}+\left(4\times 3+3^{2}-4^{2}\right)^{2}$$

Add 5 and 49 to get 54.

$$\frac{54-10}{4}+\left(4\times 3+3^{2}-4^{2}\right)^{2}$$

Subtract 10 from 54 to get 44.

$$\frac{44}{4}+\left(4\times 3+3^{2}-4^{2}\right)^{2}$$

Divide 44 by 4 to get 11.

$$11+\left(4\times 3+3^{2}-4^{2}\right)^{2}$$

Multiply 4 and 3 to get 12.

$$11+\left(12+3^{2}-4^{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$11+\left(12+9-4^{2}\right)^{2}$$

Add 12 and 9 to get 21.

$$11+\left(21-4^{2}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$11+\left(21-16\right)^{2}$$

Subtract 16 from 21 to get 5.

$$11+5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$11+25$$

Add 11 and 25 to get 36.

$$36$$

Factor

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