Solve 2^{4}:2^{3}*5+5^{3}:5^{2}-2^2*3+7^3:7^3-2^2

$$2 ^ { 4 } : 2 ^ { 3 } \times 5 + 5 ^ { 3 } : 5 ^ { 2 } - 2 ^ { 2 } \times 3 + 7 ^ { 3 } : 7 ^ { 3 } - 2 ^ { 2 }$$

Evaluate

$$0$$

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.

$$2^{1}\times 5+\frac{5^{3}}{5^{2}}-2^{2}\times 3+\frac{7^{3}}{7^{3}}-2^{2}$$

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

$$2^{1}\times 5+5^{1}-2^{2}\times 3+\frac{7^{3}}{7^{3}}-2^{2}$$

Divide 7^{3} by 7^{3} to get 1.

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

Calculate 2 to the power of 1 and get 2.

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

Multiply 2 and 5 to get 10.

$$10+5^{1}-2^{2}\times 3+1-2^{2}$$

Calculate 5 to the power of 1 and get 5.

$$10+5-2^{2}\times 3+1-2^{2}$$

Add 10 and 5 to get 15.

$$15-2^{2}\times 3+1-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$15-4\times 3+1-2^{2}$$

Multiply 4 and 3 to get 12.

$$15-12+1-2^{2}$$

Subtract 12 from 15 to get 3.

$$3+1-2^{2}$$

Add 3 and 1 to get 4.

$$4-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4-4$$

Subtract 4 from 4 to get 0.

$$0$$

Factor

$$0$$