Solve (-7a^5/6)(7a^-1/3)

$$( - 7 a ^ { 5 / 6 } ) ( 7 a ^ { - 1 / 3 } )$$

Evaluate

$$-49\sqrt{a}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{5}{6} and -\frac{1}{3} to get \frac{1}{2}.

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

Multiply -7 and 7 to get -49.

$$-49a^{\frac{1}{2}}$$

Differentiate w.r.t. a

$$-\frac{49}{2\sqrt{a}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{5}{6} and -\frac{1}{3} to get \frac{1}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-7a^{\frac{1}{2}}\times 7)$$

Multiply -7 and 7 to get -49.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-49a^{\frac{1}{2}})$$

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

$$\frac{1}{2}\left(-49\right)a^{\frac{1}{2}-1}$$

Multiply \frac{1}{2} times -49.

$$-\frac{49}{2}a^{\frac{1}{2}-1}$$

Subtract 1 from \frac{1}{2}.

$$-\frac{49}{2}a^{-\frac{1}{2}}$$