Solve 3/8a^2bdiv9/4ab^2*left(-3bright)^2

$$\frac{ 3 }{ 8 } { a }^{ 2 } b \div \frac{ 9 }{ 4 } a { b }^{ 2 } \times { \left(-3b \right) }^{ 2 }$$

Evaluate

$$\frac{3a^{3}b^{5}}{2}$$

Solution Steps

Divide \frac{3}{8}a^{2}b by \frac{9}{4} by multiplying \frac{3}{8}a^{2}b by the reciprocal of \frac{9}{4}.

$$\frac{\frac{3}{8}a^{2}b\times 4}{9}ab^{2}\left(-3b\right)^{2}$$

Multiply \frac{3}{8} and 4 to get \frac{3}{2}.

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

Divide \frac{3}{2}a^{2}b by 9 to get \frac{1}{6}a^{2}b.

$$\frac{1}{6}a^{2}bab^{2}\left(-3b\right)^{2}$$

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

$$\frac{1}{6}a^{3}bb^{2}\left(-3b\right)^{2}$$

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

$$\frac{1}{6}a^{3}b^{3}\left(-3b\right)^{2}$$

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

$$\frac{1}{6}a^{3}b^{3}\left(-3\right)^{2}b^{2}$$

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

$$\frac{1}{6}a^{3}b^{3}\times 9b^{2}$$

Multiply \frac{1}{6} and 9 to get \frac{3}{2}.

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{3}{2}a^{3}b^{5}$$

Expand

$$\frac{3a^{3}b^{5}}{2}$$

Solution Steps

Divide \frac{3}{8}a^{2}b by \frac{9}{4} by multiplying \frac{3}{8}a^{2}b by the reciprocal of \frac{9}{4}.

$$\frac{\frac{3}{8}a^{2}b\times 4}{9}ab^{2}\left(-3b\right)^{2}$$

Multiply \frac{3}{8} and 4 to get \frac{3}{2}.

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

Divide \frac{3}{2}a^{2}b by 9 to get \frac{1}{6}a^{2}b.

$$\frac{1}{6}a^{2}bab^{2}\left(-3b\right)^{2}$$

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

$$\frac{1}{6}a^{3}bb^{2}\left(-3b\right)^{2}$$

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

$$\frac{1}{6}a^{3}b^{3}\left(-3b\right)^{2}$$

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

$$\frac{1}{6}a^{3}b^{3}\left(-3\right)^{2}b^{2}$$

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

$$\frac{1}{6}a^{3}b^{3}\times 9b^{2}$$

Multiply \frac{1}{6} and 9 to get \frac{3}{2}.

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{3}{2}a^{3}b^{5}$$