Solve 910^9310^-6910^-6/0.11^2

$$\frac{ 9 { 10 }^{ 9 } 3 { 10 }^{ -6 } 9 { 10 }^{ -6 } }{ { 0.11 }^{ 2 } }$$

Evaluate

$$\frac{2430}{121}\approx 20.082644628$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and -6 to get 3.

$$\frac{9\times 10^{3}\times 3\times 9\times 10^{-6}}{0.11^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and -6 to get -3.

$$\frac{9\times 10^{-3}\times 3\times 9}{0.11^{2}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{9\times \frac{1}{1000}\times 3\times 9}{0.11^{2}}$$

Multiply 9 and \frac{1}{1000} to get \frac{9}{1000}.

$$\frac{\frac{9}{1000}\times 3\times 9}{0.11^{2}}$$

Multiply \frac{9}{1000} and 3 to get \frac{27}{1000}.

$$\frac{\frac{27}{1000}\times 9}{0.11^{2}}$$

Multiply \frac{27}{1000} and 9 to get \frac{243}{1000}.

$$\frac{\frac{243}{1000}}{0.11^{2}}$$

Calculate 0.11 to the power of 2 and get 0.0121.

$$\frac{\frac{243}{1000}}{0.0121}$$

Express \frac{\frac{243}{1000}}{0.0121} as a single fraction.

$$\frac{243}{1000\times 0.0121}$$

Multiply 1000 and 0.0121 to get 12.1.

$$\frac{243}{12.1}$$

Expand \frac{243}{12.1} by multiplying both numerator and the denominator by 10.

$$\frac{2430}{121}$$

Factor

$$\frac{2 \cdot 5 \cdot 3 ^ {5}}{11 ^ {2}} = 20\frac{10}{121} = 20.082644628099175$$