Solve =(a*10^9)(1.0*10^-2)(1.0*10^-2)/3^2

$$= \frac { ( a \times 10 ^ { 9 } ) ( 1.0 \times 10 ^ { - 2 } ) ( 1.0 \times 10 ^ { - 2 } ) } { 3 ^ { 2 } }$$

Evaluate

$$\frac{100000a}{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and -2 to get 7.

$$\frac{a\times 10^{7}\times 1\times 1\times 10^{-2}}{3^{2}}$$

To multiply powers of the same base, add their exponents. Add 7 and -2 to get 5.

$$\frac{a\times 10^{5}\times 1\times 1}{3^{2}}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{a\times 100000\times 1\times 1}{3^{2}}$$

Multiply 100000 and 1 to get 100000.

$$\frac{a\times 100000\times 1}{3^{2}}$$

Multiply 100000 and 1 to get 100000.

$$\frac{a\times 100000}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{a\times 100000}{9}$$

Differentiate w.r.t. a

$$\frac{100000}{9} = 11111\frac{1}{9} = 11111.111111111111$$