Solve -4/15b^2x^5div-36/5b^3x^2

$$\frac { - 4 } { 15 } b ^ { 2 } x ^ { 5 } \div \frac { - 36 } { 5 } b ^ { 3 } x ^ { 2 }$$

Evaluate

$$\frac{b^{5}x^{7}}{27}$$

Solution Steps

Fraction \frac{-4}{15} can be rewritten as -\frac{4}{15} by extracting the negative sign.

$$\frac{-\frac{4}{15}b^{2}x^{5}}{\frac{-36}{5}}b^{3}x^{2}$$

Fraction \frac{-36}{5} can be rewritten as -\frac{36}{5} by extracting the negative sign.

$$\frac{-\frac{4}{15}b^{2}x^{5}}{-\frac{36}{5}}b^{3}x^{2}$$

Divide -\frac{4}{15}b^{2}x^{5} by -\frac{36}{5} by multiplying -\frac{4}{15}b^{2}x^{5} by the reciprocal of -\frac{36}{5}.

$$\frac{-\frac{4}{15}b^{2}x^{5}\times 5}{-36}b^{3}x^{2}$$

Multiply -\frac{4}{15} and 5 to get -\frac{4}{3}.

$$\frac{-\frac{4}{3}b^{2}x^{5}}{-36}b^{3}x^{2}$$

Divide -\frac{4}{3}b^{2}x^{5} by -36 to get \frac{1}{27}b^{2}x^{5}.

$$\frac{1}{27}b^{2}x^{5}b^{3}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{1}{27}b^{5}x^{5}x^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{1}{27}b^{5}x^{7}$$

Differentiate w.r.t. x

$$\frac{7b^{5}x^{6}}{27}$$