Solve (-9/5a^2c)*(-3/5ab^2)*(-5/27b^2)

$$( - \frac { 9 } { 5 } a ^ { 2 } c ) \cdot ( - \frac { 3 } { 5 } a b ^ { 2 } ) \cdot ( - \frac { 5 } { 27 } b ^ { 2 } )$$

Evaluate

$$-\frac{ca^{3}b^{4}}{5}$$

Solution Steps

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

$$-\frac{9}{5}a^{3}c\left(-\frac{3}{5}\right)b^{2}\left(-\frac{5}{27}\right)b^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-\frac{9}{5}a^{3}c\left(-\frac{3}{5}\right)b^{4}\left(-\frac{5}{27}\right)$$

Multiply -\frac{9}{5} and -\frac{3}{5} to get \frac{27}{25}.

$$\frac{27}{25}a^{3}cb^{4}\left(-\frac{5}{27}\right)$$

Multiply \frac{27}{25} and -\frac{5}{27} to get -\frac{1}{5}.

$$-\frac{1}{5}a^{3}cb^{4}$$

Differentiate w.r.t. c

$$-\frac{a^{3}b^{4}}{5}$$