Solve x^2/7*7^-4=

$$\frac { x ^ { 2 } } { 7 \times 7 ^ { - 4 } } =$$

Evaluate

$$343x^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -4 to get -3.

$$\frac{x^{2}}{7^{-3}}$$

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

$$\frac{x^{2}}{\frac{1}{343}}$$

Divide x^{2} by \frac{1}{343} by multiplying x^{2} by the reciprocal of \frac{1}{343}.

$$x^{2}\times 343$$

Differentiate w.r.t. x

$$686x$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and -4 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}}{7^{-3}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}}{\frac{1}{343}})$$

Divide x^{2} by \frac{1}{343} by multiplying x^{2} by the reciprocal of \frac{1}{343}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\times 343)$$

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

$$2\times 343x^{2-1}$$

Multiply 2 times 343.

$$686x^{2-1}$$

Subtract 1 from 2.

$$686x^{1}$$

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

$$686x$$