Solve 5^{3}:5^{2}-(5^2*5)^4:(5^9*5^2)

$$5 ^ { 3 } : 5 ^ { 2 } - ( 5 ^ { 2 } \cdot 5 ) ^ { 4 } : ( 5 ^ { 9 } \cdot 5 ^ { 2 } )$$

Evaluate

$$0$$

Solution Steps

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

$$5^{1}-\frac{\left(5^{2}\times 5\right)^{4}}{5^{9}\times 5^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$5^{1}-\frac{\left(5^{3}\right)^{4}}{5^{9}\times 5^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$5^{1}-\frac{5^{12}}{5^{9}\times 5^{2}}$$

To multiply powers of the same base, add their exponents. Add 9 and 2 to get 11.

$$5^{1}-\frac{5^{12}}{5^{11}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 11 from 12 to get 1.

$$5^{1}-5^{1}$$

Calculate 5 to the power of 1 and get 5.

$$5-5^{1}$$

Calculate 5 to the power of 1 and get 5.

$$5-5$$

Subtract 5 from 5 to get 0.

$$0$$

Factor

$$0$$