Solve (2a^{2}b)^2div(ab)^3*(3a^3b^2)

$$( 2 a ^ { 2 } b ) ^ { 2 } \div ( a b ) ^ { 3 } \times ( 3 a ^ { 3 } b ^ { 2 } )$$

Evaluate

$$12ba^{4}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

$$\frac{4a^{4}b^{2}}{a^{3}b^{3}}\times 3a^{3}b^{2}$$

Cancel out b^{2}a^{3} in both numerator and denominator.

$$\frac{4a}{b}\times 3a^{3}b^{2}$$

Express \frac{4a}{b}\times 3 as a single fraction.

$$\frac{4a\times 3}{b}a^{3}b^{2}$$

Express \frac{4a\times 3}{b}a^{3} as a single fraction.

$$\frac{4a\times 3a^{3}}{b}b^{2}$$

Express \frac{4a\times 3a^{3}}{b}b^{2} as a single fraction.

$$\frac{4a\times 3a^{3}b^{2}}{b}$$

Cancel out b in both numerator and denominator.

$$3\times 4aba^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$3\times 4a^{4}b$$

Multiply 3 and 4 to get 12.

$$12a^{4}b$$

Expand

$$12ba^{4}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

$$\frac{4a^{4}b^{2}}{a^{3}b^{3}}\times 3a^{3}b^{2}$$

Cancel out b^{2}a^{3} in both numerator and denominator.

$$\frac{4a}{b}\times 3a^{3}b^{2}$$

Express \frac{4a}{b}\times 3 as a single fraction.

$$\frac{4a\times 3}{b}a^{3}b^{2}$$

Express \frac{4a\times 3}{b}a^{3} as a single fraction.

$$\frac{4a\times 3a^{3}}{b}b^{2}$$

Express \frac{4a\times 3a^{3}}{b}b^{2} as a single fraction.

$$\frac{4a\times 3a^{3}b^{2}}{b}$$

Cancel out b in both numerator and denominator.

$$3\times 4aba^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$3\times 4a^{4}b$$

Multiply 3 and 4 to get 12.

$$12a^{4}b$$