Solve 8*9a*10^9(-8*10^6/5*10^-212)

$$8 \cdot 9 a \times 10 ^ { 9 } ( \frac { - 8 \times 10 ^ { 6 } } { 5 \times 10 ^ { - 212 } } )$$

Evaluate

$$-11520000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a$$

Solution Steps

Multiply 8 and 9 to get 72.

$$72a\times 10^{9}\times \frac{-8\times 10^{6}}{5\times 10^{-212}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$72a\times 1000000000\times \frac{-8\times 10^{6}}{5\times 10^{-212}}$$

Multiply 72 and 1000000000 to get 72000000000.

$$72000000000a\times \frac{-8\times 10^{6}}{5\times 10^{-212}}$$

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

$$72000000000a\times \frac{-8\times 10^{218}}{5}$$

Calculate 10 to the power of 218 and get 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$72000000000a\times \frac{-8\times 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{5}$$

Multiply -8 and 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 to get -800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$72000000000a\times \frac{-800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{5}$$

Divide -800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 by 5 to get -160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$72000000000a\left(-160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)$$

Multiply 72000000000 and -160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 to get -11520000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$-11520000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a$$

Differentiate w.r.t. a

$$-11520000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$$

Steps Using Definition of a Derivative

Multiply 8 and 9 to get 72.

$$\frac{\mathrm{d}}{\mathrm{d}a}(72a\times 10^{9}\times \frac{-8\times 10^{6}}{5\times 10^{-212}})$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{\mathrm{d}}{\mathrm{d}a}(72a\times 1000000000\times \frac{-8\times 10^{6}}{5\times 10^{-212}})$$

Multiply 72 and 1000000000 to get 72000000000.

$$\frac{\mathrm{d}}{\mathrm{d}a}(72000000000a\times \frac{-8\times 10^{6}}{5\times 10^{-212}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(72000000000a\times \frac{-8\times 10^{218}}{5})$$

Calculate 10 to the power of 218 and get 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}a}(72000000000a\times \frac{-8\times 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{5})$$

Multiply -8 and 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 to get -800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}a}(72000000000a\times \frac{-800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{5})$$

Divide -800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 by 5 to get -160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}a}(72000000000a\left(-160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right))$$

Multiply 72000000000 and -160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 to get -11520000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-11520000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a)$$

The derivative of ax^{n} is nax^{n-1}.

$$-11520000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a^{1-1}$$

Subtract 1 from 1.

$$-11520000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a^{0}$$

For any term t except 0, t^{0}=1.

$$-11520000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$$