Solve 3^{2}:3+4^{2}:4^{2}+(5^2*2-50):2^2-3^3:3^2

$$3 ^ { 2 } : 3 + 4 ^ { 2 } : 4 ^ { 2 } + ( 5 ^ { 2 } \cdot 2 - 50 ) : 2 ^ { 2 } - 3 ^ { 3 } : 3 ^ { 2 }$$

Evaluate

$$1$$

Solution Steps

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

$$3^{1}+\frac{4^{2}}{4^{2}}+\frac{5^{2}\times 2-50}{2^{2}}-\frac{3^{3}}{3^{2}}$$

Divide 4^{2} by 4^{2} to get 1.

$$3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-\frac{3^{3}}{3^{2}}$$

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

$$3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{1}$$

Calculate 3 to the power of 1 and get 3.

$$3+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{1}$$

Add 3 and 1 to get 4.

$$4+\frac{5^{2}\times 2-50}{2^{2}}-3^{1}$$

Calculate 5 to the power of 2 and get 25.

$$4+\frac{25\times 2-50}{2^{2}}-3^{1}$$

Multiply 25 and 2 to get 50.

$$4+\frac{50-50}{2^{2}}-3^{1}$$

Subtract 50 from 50 to get 0.

$$4+\frac{0}{2^{2}}-3^{1}$$

Calculate 2 to the power of 2 and get 4.

$$4+\frac{0}{4}-3^{1}$$

Zero divided by any non-zero number gives zero.

$$4+0-3^{1}$$

Add 4 and 0 to get 4.

$$4-3^{1}$$

Calculate 3 to the power of 1 and get 3.

$$4-3$$

Subtract 3 from 4 to get 1.

$$1$$

Factor

$$1$$