Solve (2a^{2}b^3)^4:(-3ab^4)^2=

$$( 2 a ^ { 2 } b ^ { 3 } ) ^ { 4 } : ( - 3 a b ^ { 4 } ) ^ { 2 } =$$

Evaluate

$$\frac{16b^{4}a^{6}}{9}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{2^{4}a^{8}b^{12}}{\left(-3ab^{4}\right)^{2}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16a^{8}b^{12}}{\left(-3ab^{4}\right)^{2}}$$

Expand \left(-3ab^{4}\right)^{2}.

$$\frac{16a^{8}b^{12}}{\left(-3\right)^{2}a^{2}\left(b^{4}\right)^{2}}$$

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

$$\frac{16a^{8}b^{12}}{\left(-3\right)^{2}a^{2}b^{8}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{16a^{8}b^{12}}{9a^{2}b^{8}}$$

Cancel out a^{2}b^{8} in both numerator and denominator.

$$\frac{16b^{4}a^{6}}{9}$$

Expand

$$\frac{16b^{4}a^{6}}{9}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{2^{4}a^{8}b^{12}}{\left(-3ab^{4}\right)^{2}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16a^{8}b^{12}}{\left(-3ab^{4}\right)^{2}}$$

Expand \left(-3ab^{4}\right)^{2}.

$$\frac{16a^{8}b^{12}}{\left(-3\right)^{2}a^{2}\left(b^{4}\right)^{2}}$$

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

$$\frac{16a^{8}b^{12}}{\left(-3\right)^{2}a^{2}b^{8}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{16a^{8}b^{12}}{9a^{2}b^{8}}$$

Cancel out a^{2}b^{8} in both numerator and denominator.

$$\frac{16b^{4}a^{6}}{9}$$