Solve frac{(64b^9)^-frac{1{3}}*b}{B}

$$\frac { ( 64 b ^ { 9 } ) ^ { - \frac { 1 } { 3 } } \cdot b } { B }$$

Evaluate

$$\frac{1}{4Bb^{2}}$$

Solution Steps

Expand \left(64b^{9}\right)^{-\frac{1}{3}}.

$$\frac{64^{-\frac{1}{3}}\left(b^{9}\right)^{-\frac{1}{3}}b}{B}$$

To raise a power to another power, multiply the exponents. Multiply 9 and -\frac{1}{3} to get -3.

$$\frac{64^{-\frac{1}{3}}b^{-3}b}{B}$$

Calculate 64 to the power of -\frac{1}{3} and get \frac{1}{4}.

$$\frac{\frac{1}{4}b^{-3}b}{B}$$

To multiply powers of the same base, add their exponents. Add -3 and 1 to get -2.

$$\frac{\frac{1}{4}b^{-2}}{B}$$

Differentiate w.r.t. b

$$-\frac{1}{2Bb^{3}}$$