Solve 2ab^2*(3b)^2div(-3ab)^2

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

Evaluate

$$\frac{2b^{2}}{a}$$

Solution Steps

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

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

Calculate 3 to the power of 2 and get 9.

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

Multiply 2 and 9 to get 18.

$$\frac{18ab^{2}b^{2}}{\left(-3ab\right)^{2}}$$

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

$$\frac{18ab^{4}}{\left(-3ab\right)^{2}}$$

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

$$\frac{18ab^{4}}{\left(-3\right)^{2}a^{2}b^{2}}$$

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

$$\frac{18ab^{4}}{9a^{2}b^{2}}$$

Cancel out 9ab^{2} in both numerator and denominator.

$$\frac{2b^{2}}{a}$$

Expand

$$\frac{2b^{2}}{a}$$

Solution Steps

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

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

Calculate 3 to the power of 2 and get 9.

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

Multiply 2 and 9 to get 18.

$$\frac{18ab^{2}b^{2}}{\left(-3ab\right)^{2}}$$

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

$$\frac{18ab^{4}}{\left(-3ab\right)^{2}}$$

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

$$\frac{18ab^{4}}{\left(-3\right)^{2}a^{2}b^{2}}$$

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

$$\frac{18ab^{4}}{9a^{2}b^{2}}$$

Cancel out 9ab^{2} in both numerator and denominator.

$$\frac{2b^{2}}{a}$$