Solve (-2/3a^{3}b)^{3}:(+2/3a^{2}b)^{2}]^{3}+1/2a^{2}b^4:(-2a^2b)*[(-a)^5]^3

$$( - \frac { 2 } { 3 } a ^ { 3 } b ) ^ { 3 } : ( + \frac { 2 } { 3 } a ^ { 2 } b ) ^ { 2 } ] ^ { 3 } + \frac { 1 } { 2 } a ^ { 2 } b ^ { 4 } : ( - 2 a ^ { 2 } b ) \cdot [ ( - a ) ^ { 5 } ] ^ { 3 }$$

Evaluate

$$-\frac{2ba^{5}}{3}$$

Solution Steps

Expand \left(-\frac{2}{3}a^{3}b\right)^{3}.

$$\frac{\left(-\frac{2}{3}\right)^{3}\left(a^{3}\right)^{3}b^{3}}{\left(\frac{2}{3}a^{2}b\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

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

Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.

$$\frac{-\frac{8}{27}a^{9}b^{3}}{\left(\frac{2}{3}a^{2}b\right)^{2}}$$

Expand \left(\frac{2}{3}a^{2}b\right)^{2}.

$$\frac{-\frac{8}{27}a^{9}b^{3}}{\left(\frac{2}{3}\right)^{2}\left(a^{2}\right)^{2}b^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{-\frac{8}{27}a^{9}b^{3}}{\left(\frac{2}{3}\right)^{2}a^{4}b^{2}}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{-\frac{8}{27}a^{9}b^{3}}{\frac{4}{9}a^{4}b^{2}}$$

Cancel out b^{2}a^{4} in both numerator and denominator.

$$\frac{-\frac{8}{27}ba^{5}}{\frac{4}{9}}$$

Divide -\frac{8}{27}ba^{5} by \frac{4}{9} by multiplying -\frac{8}{27}ba^{5} by the reciprocal of \frac{4}{9}.

$$\frac{-\frac{8}{27}ba^{5}\times 9}{4}$$

Multiply -\frac{8}{27} and 9 to get -\frac{8}{3}.

$$\frac{-\frac{8}{3}ba^{5}}{4}$$

Divide -\frac{8}{3}ba^{5} by 4 to get -\frac{2}{3}ba^{5}.

$$-\frac{2}{3}ba^{5}$$

Expand

$$-\frac{2ba^{5}}{3}$$

Solution Steps

Expand \left(-\frac{2}{3}a^{3}b\right)^{3}.

$$\frac{\left(-\frac{2}{3}\right)^{3}\left(a^{3}\right)^{3}b^{3}}{\left(\frac{2}{3}a^{2}b\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

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

Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.

$$\frac{-\frac{8}{27}a^{9}b^{3}}{\left(\frac{2}{3}a^{2}b\right)^{2}}$$

Expand \left(\frac{2}{3}a^{2}b\right)^{2}.

$$\frac{-\frac{8}{27}a^{9}b^{3}}{\left(\frac{2}{3}\right)^{2}\left(a^{2}\right)^{2}b^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{-\frac{8}{27}a^{9}b^{3}}{\left(\frac{2}{3}\right)^{2}a^{4}b^{2}}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{-\frac{8}{27}a^{9}b^{3}}{\frac{4}{9}a^{4}b^{2}}$$

Cancel out b^{2}a^{4} in both numerator and denominator.

$$\frac{-\frac{8}{27}ba^{5}}{\frac{4}{9}}$$

Divide -\frac{8}{27}ba^{5} by \frac{4}{9} by multiplying -\frac{8}{27}ba^{5} by the reciprocal of \frac{4}{9}.

$$\frac{-\frac{8}{27}ba^{5}\times 9}{4}$$

Multiply -\frac{8}{27} and 9 to get -\frac{8}{3}.

$$\frac{-\frac{8}{3}ba^{5}}{4}$$

Divide -\frac{8}{3}ba^{5} by 4 to get -\frac{2}{3}ba^{5}.

$$-\frac{2}{3}ba^{5}$$