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

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

Evaluate

$$29$$

Solution Steps

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

$$\frac{\frac{5^{3}\times 2-2\times 10^{2}}{5}}{\frac{10^{6}}{10^{5}}}+\frac{7^{3}}{7^{2}}\times 2^{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 6 to get 1.

$$\frac{\frac{5^{3}\times 2-2\times 10^{2}}{5}}{10^{1}}+\frac{7^{3}}{7^{2}}\times 2^{2}$$

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

$$\frac{\frac{5^{3}\times 2-2\times 10^{2}}{5}}{10^{1}}+7^{1}\times 2^{2}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{\frac{125\times 2-2\times 10^{2}}{5}}{10^{1}}+7^{1}\times 2^{2}$$

Multiply 125 and 2 to get 250.

$$\frac{\frac{250-2\times 10^{2}}{5}}{10^{1}}+7^{1}\times 2^{2}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{\frac{250-2\times 100}{5}}{10^{1}}+7^{1}\times 2^{2}$$

Multiply 2 and 100 to get 200.

$$\frac{\frac{250-200}{5}}{10^{1}}+7^{1}\times 2^{2}$$

Subtract 200 from 250 to get 50.

$$\frac{\frac{50}{5}}{10^{1}}+7^{1}\times 2^{2}$$

Divide 50 by 5 to get 10.

$$\frac{10}{10^{1}}+7^{1}\times 2^{2}$$

Calculate 10 to the power of 1 and get 10.

$$\frac{10}{10}+7^{1}\times 2^{2}$$

Divide 10 by 10 to get 1.

$$1+7^{1}\times 2^{2}$$

Calculate 7 to the power of 1 and get 7.

$$1+7\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$1+7\times 4$$

Multiply 7 and 4 to get 28.

$$1+28$$

Add 1 and 28 to get 29.

$$29$$

Factor

$$29$$