Solve 5^4*5^4*5/(5*5^4)^3

$$\frac { 5 ^ { 4 } * 5 ^ { 4 } * 5 } { ( 5 * 5 ^ { 4 } ) ^ { 3 } }$$

Evaluate

$$\frac{1}{15625}=0.000064$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{5^{8}\times 5}{\left(5\times 5^{4}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

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

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{5^{9}}{\left(5^{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{5^{9}}{5^{15}}$$

Rewrite 5^{15} as 5^{9}\times 5^{6}. Cancel out 5^{9} in both numerator and denominator.

$$\frac{1}{5^{6}}$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{1}{15625}$$

Factor

$$\frac{1}{5 ^ {6}} = 6.3999999999999995 \times 10^{-5}$$