Solve (5)3a^2*(-1/8ab)*(-2a^2b)^3

$$( 5 ) 3 a ^ { 2 } \cdot ( - \frac { 1 } { 8 } a b ) \cdot ( - 2 a ^ { 2 } b ) ^ { 3 }$$

Evaluate

$$15b^{4}a^{9}$$

Solution Steps

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

$$5\times 3a^{3}\left(-\frac{1}{8}\right)b\left(-2a^{2}b\right)^{3}$$

Multiply 5 and 3 to get 15.

$$15a^{3}\left(-\frac{1}{8}\right)b\left(-2a^{2}b\right)^{3}$$

Multiply 15 and -\frac{1}{8} to get -\frac{15}{8}.

$$-\frac{15}{8}a^{3}b\left(-2a^{2}b\right)^{3}$$

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

$$-\frac{15}{8}a^{3}b\left(-2\right)^{3}\left(a^{2}\right)^{3}b^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$-\frac{15}{8}a^{3}b\left(-2\right)^{3}a^{6}b^{3}$$

Calculate -2 to the power of 3 and get -8.

$$-\frac{15}{8}a^{3}b\left(-8\right)a^{6}b^{3}$$

Multiply -\frac{15}{8} and -8 to get 15.

$$15a^{3}ba^{6}b^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$15a^{9}bb^{3}$$

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

$$15a^{9}b^{4}$$

Expand

$$15b^{4}a^{9}$$

Solution Steps

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

$$5\times 3a^{3}\left(-\frac{1}{8}\right)b\left(-2a^{2}b\right)^{3}$$

Multiply 5 and 3 to get 15.

$$15a^{3}\left(-\frac{1}{8}\right)b\left(-2a^{2}b\right)^{3}$$

Multiply 15 and -\frac{1}{8} to get -\frac{15}{8}.

$$-\frac{15}{8}a^{3}b\left(-2a^{2}b\right)^{3}$$

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

$$-\frac{15}{8}a^{3}b\left(-2\right)^{3}\left(a^{2}\right)^{3}b^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$-\frac{15}{8}a^{3}b\left(-2\right)^{3}a^{6}b^{3}$$

Calculate -2 to the power of 3 and get -8.

$$-\frac{15}{8}a^{3}b\left(-8\right)a^{6}b^{3}$$

Multiply -\frac{15}{8} and -8 to get 15.

$$15a^{3}ba^{6}b^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$15a^{9}bb^{3}$$

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

$$15a^{9}b^{4}$$