Solve (-2a)^2div6ab^2*9b

$$( - 2 a ) ^ { 2 } \div 6 a b ^ { 2 } \times 9 b$$

Evaluate

$$6\left(ab\right)^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\left(-2a\right)^{2}}{6}ab^{3}\times 9$$

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

$$\frac{\left(-2\right)^{2}a^{2}}{6}ab^{3}\times 9$$

Calculate -2 to the power of 2 and get 4.

$$\frac{4a^{2}}{6}ab^{3}\times 9$$

Divide 4a^{2} by 6 to get \frac{2}{3}a^{2}.

$$\frac{2}{3}a^{2}ab^{3}\times 9$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{2}{3}a^{3}b^{3}\times 9$$

Multiply \frac{2}{3} and 9 to get 6.

$$6a^{3}b^{3}$$

Expand

$$6\left(ab\right)^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\left(-2a\right)^{2}}{6}ab^{3}\times 9$$

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

$$\frac{\left(-2\right)^{2}a^{2}}{6}ab^{3}\times 9$$

Calculate -2 to the power of 2 and get 4.

$$\frac{4a^{2}}{6}ab^{3}\times 9$$

Divide 4a^{2} by 6 to get \frac{2}{3}a^{2}.

$$\frac{2}{3}a^{2}ab^{3}\times 9$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{2}{3}a^{3}b^{3}\times 9$$

Multiply \frac{2}{3} and 9 to get 6.

$$6a^{3}b^{3}$$