Solve (2a^{3}b^4)^2div(-3a^2b^5)

$$( 2 a ^ { 3 } b ^ { 4 } ) ^ { 2 } \div ( - 3 a ^ { 2 } b ^ { 5 } )$$

Evaluate

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

Solution Steps

Expand \left(2a^{3}b^{4}\right)^{2}.

$$\frac{2^{2}\left(a^{3}\right)^{2}\left(b^{4}\right)^{2}}{-3a^{2}b^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{2^{2}a^{6}\left(b^{4}\right)^{2}}{-3a^{2}b^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{2^{2}a^{6}b^{8}}{-3a^{2}b^{5}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{6}b^{8}}{-3a^{2}b^{5}}$$

Cancel out a^{2}b^{5} in both numerator and denominator.

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

Expand

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

Solution Steps

Expand \left(2a^{3}b^{4}\right)^{2}.

$$\frac{2^{2}\left(a^{3}\right)^{2}\left(b^{4}\right)^{2}}{-3a^{2}b^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{2^{2}a^{6}\left(b^{4}\right)^{2}}{-3a^{2}b^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{2^{2}a^{6}b^{8}}{-3a^{2}b^{5}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{6}b^{8}}{-3a^{2}b^{5}}$$

Cancel out a^{2}b^{5} in both numerator and denominator.

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