Solve frac{5^{8}*5^{2}*5^4}{5^7*5^4*5^6}

$$\frac { 5 ^ { 8 } \cdot 5 ^ { 2 } \cdot 5 ^ { 4 } } { 5 ^ { 7 } \cdot 5 ^ { 4 } \cdot 5 ^ { 6 } }$$

Evaluate

$$\frac{1}{125}=0.008$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$\frac{5^{10}\times 5^{4}}{5^{7}\times 5^{4}\times 5^{6}}$$

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$\frac{5^{14}}{5^{7}\times 5^{4}\times 5^{6}}$$

To multiply powers of the same base, add their exponents. Add 7 and 4 to get 11.

$$\frac{5^{14}}{5^{11}\times 5^{6}}$$

To multiply powers of the same base, add their exponents. Add 11 and 6 to get 17.

$$\frac{5^{14}}{5^{17}}$$

Rewrite 5^{17} as 5^{14}\times 5^{3}. Cancel out 5^{14} in both numerator and denominator.

$$\frac{1}{5^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{1}{125}$$

Factor

$$\frac{1}{5 ^ {3}} = 0.008$$