Solve 25left(10^2right)^-3121/11*7510^-9

$$\frac{ 25 { \left( { 10 }^{ 2 } \right) }^{ -3 } 121 }{ 11 \cdot 75 { 10 }^{ -9 } }$$

Evaluate

$$\frac{11000}{3}\approx 3666.666666667$$

Solution Steps

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

$$\frac{25\times 10^{-6}\times 121}{11\times 75\times 10^{-9}}$$

Cancel out 11\times 25 in both numerator and denominator.

$$\frac{11\times 10^{-6}}{3\times 10^{-9}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{11\times 10^{3}}{3}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{11\times 1000}{3}$$

Multiply 11 and 1000 to get 11000.

$$\frac{11000}{3}$$

Factor

$$\frac{2 ^ {3} \cdot 5 ^ {3} \cdot 11}{3} = 3666\frac{2}{3} = 3666.6666666666665$$