Solve 10^-3*10^-6*10/10^810^-2

$$\frac{ { 10 }^{ -3 } \times { 10 }^{ -6 } \times 10 }{ { 10 }^{ 8 } { 10 }^{ -2 } }$$

Evaluate

$$\frac{1}{100000000000000}= 10^{-14}$$

Solution Steps

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

$$\frac{10^{-9}\times 10}{10^{8}\times 10^{-2}}$$

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

$$\frac{10^{-8}}{10^{8}\times 10^{-2}}$$

To multiply powers of the same base, add their exponents. Add 8 and -2 to get 6.

$$\frac{10^{-8}}{10^{6}}$$

Rewrite 10^{6} as 10^{-8}\times 10^{14}. Cancel out 10^{-8} in both numerator and denominator.

$$\frac{1}{10^{14}}$$

Calculate 10 to the power of 14 and get 100000000000000.

$$\frac{1}{100000000000000}$$

Factor

$$\frac{1}{2 ^ {14} \cdot 5 ^ {14}} = 1 \times 10^{-14}$$