Solve (2^{2}+5^{4}:5^{2}-5)-2*3^{2}+(2^{2})^3:4^3-1+2^2*2^2

$$( 2 ^ { 2 } + 5 ^ { 4 } : 5 ^ { 2 } - 5 ) - 2 \times 3 ^ { 2 } + ( 2 ^ { 2 } ) ^ { 3 } : 4 ^ { 3 } - 1 + 2 ^ { 2 } \times 2 ^ { 2 }$$

Evaluate

$$22$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$2^{2}+5^{2}-5-2\times 3^{2}+\frac{2^{6}}{4^{3}}-1+2^{2}\times 2^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$2^{2}+5^{2}-5-2\times 3^{2}+\frac{2^{6}}{4^{3}}-1+2^{4}$$

Calculate 2 to the power of 2 and get 4.

$$4+5^{2}-5-2\times 3^{2}+\frac{2^{6}}{4^{3}}-1+2^{4}$$

Calculate 5 to the power of 2 and get 25.

$$4+25-5-2\times 3^{2}+\frac{2^{6}}{4^{3}}-1+2^{4}$$

Add 4 and 25 to get 29.

$$29-5-2\times 3^{2}+\frac{2^{6}}{4^{3}}-1+2^{4}$$

Subtract 5 from 29 to get 24.

$$24-2\times 3^{2}+\frac{2^{6}}{4^{3}}-1+2^{4}$$

Calculate 3 to the power of 2 and get 9.

$$24-2\times 9+\frac{2^{6}}{4^{3}}-1+2^{4}$$

Multiply 2 and 9 to get 18.

$$24-18+\frac{2^{6}}{4^{3}}-1+2^{4}$$

Subtract 18 from 24 to get 6.

$$6+\frac{2^{6}}{4^{3}}-1+2^{4}$$

Calculate 2 to the power of 6 and get 64.

$$6+\frac{64}{4^{3}}-1+2^{4}$$

Calculate 4 to the power of 3 and get 64.

$$6+\frac{64}{64}-1+2^{4}$$

Divide 64 by 64 to get 1.

$$6+1-1+2^{4}$$

Add 6 and 1 to get 7.

$$7-1+2^{4}$$

Subtract 1 from 7 to get 6.

$$6+2^{4}$$

Calculate 2 to the power of 4 and get 16.

$$6+16$$

Add 6 and 16 to get 22.

$$22$$

Factor

$$2\times 11$$