Solve 49*t^-3/7^-3*10*t^-5

$$\frac { 49 \times t ^ { - 3 } } { 7 ^ { - 3 } \times 10 \times t ^ { - 5 } }$$

Evaluate

$$\frac{16807t^{2}}{10}$$

Solution Steps

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

$$\frac{49t^{2}}{10\times 7^{-3}}$$

Calculate 7 to the power of -3 and get \frac{1}{343}.

$$\frac{49t^{2}}{10\times \frac{1}{343}}$$

Multiply 10 and \frac{1}{343} to get \frac{10}{343}.

$$\frac{49t^{2}}{\frac{10}{343}}$$

Divide 49t^{2} by \frac{10}{343} by multiplying 49t^{2} by the reciprocal of \frac{10}{343}.

$$\frac{49t^{2}\times 343}{10}$$

Multiply 49 and 343 to get 16807.

$$\frac{16807t^{2}}{10}$$

Differentiate w.r.t. t

$$\frac{16807t}{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{49}{\frac{10}{343}}t^{-3-\left(-5\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{16807}{10}t^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times \frac{16807}{10}t^{2-1}$$

Do the arithmetic.

$$\frac{16807}{5}t^{1}$$

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

$$\frac{16807}{5}t$$