Solve (-3/2ab^2c^4)^3

$$( - \frac { 3 } { 2 } a b ^ { 2 } c ^ { 4 } ) ^ { 3 }$$

Evaluate

$$-\frac{27a^{3}b^{6}c^{12}}{8}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(-\frac{3}{2}a^{1}b^{2}c^{4}\right)^{3}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-\frac{3}{2}\right)^{3}\left(a^{1}\right)^{3}\left(b^{2}\right)^{3}\left(c^{4}\right)^{3}$$

Raise -\frac{3}{2} to the power 3.

$$-\frac{27}{8}\left(a^{1}\right)^{3}\left(b^{2}\right)^{3}\left(c^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents.

$$-\frac{27}{8}a^{3}b^{2\times 3}c^{4\times 3}$$

Multiply 2 times 3.

$$-\frac{27}{8}a^{3}b^{6}c^{4\times 3}$$

Multiply 4 times 3.

$$-\frac{27}{8}a^{3}b^{6}c^{12}$$

Expand

$$-\frac{27a^{3}b^{6}c^{12}}{8}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(-\frac{3}{2}a^{1}b^{2}c^{4}\right)^{3}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-\frac{3}{2}\right)^{3}\left(a^{1}\right)^{3}\left(b^{2}\right)^{3}\left(c^{4}\right)^{3}$$

Raise -\frac{3}{2} to the power 3.

$$-\frac{27}{8}\left(a^{1}\right)^{3}\left(b^{2}\right)^{3}\left(c^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents.

$$-\frac{27}{8}a^{3}b^{2\times 3}c^{4\times 3}$$

Multiply 2 times 3.

$$-\frac{27}{8}a^{3}b^{6}c^{4\times 3}$$

Multiply 4 times 3.

$$-\frac{27}{8}a^{3}b^{6}c^{12}$$