Solve (-2/3a^6b^2c^3)^4

$$( - \frac { 2 } { 3 } a ^ { 6 } b ^ { 2 } c ^ { 3 } ) ^ { 4 }$$

Evaluate

$$\frac{16b^{8}c^{12}a^{24}}{81}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(-\frac{2}{3}a^{6}b^{2}c^{3}\right)^{4}$$

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

$$\left(-\frac{2}{3}\right)^{4}\left(a^{6}\right)^{4}\left(b^{2}\right)^{4}\left(c^{3}\right)^{4}$$

Raise -\frac{2}{3} to the power 4.

$$\frac{16}{81}\left(a^{6}\right)^{4}\left(b^{2}\right)^{4}\left(c^{3}\right)^{4}$$

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

$$\frac{16}{81}a^{6\times 4}b^{2\times 4}c^{3\times 4}$$

Multiply 6 times 4.

$$\frac{16}{81}a^{24}b^{2\times 4}c^{3\times 4}$$

Multiply 2 times 4.

$$\frac{16}{81}a^{24}b^{8}c^{3\times 4}$$

Multiply 3 times 4.

$$\frac{16}{81}a^{24}b^{8}c^{12}$$

Expand

$$\frac{16b^{8}c^{12}a^{24}}{81}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(-\frac{2}{3}a^{6}b^{2}c^{3}\right)^{4}$$

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

$$\left(-\frac{2}{3}\right)^{4}\left(a^{6}\right)^{4}\left(b^{2}\right)^{4}\left(c^{3}\right)^{4}$$

Raise -\frac{2}{3} to the power 4.

$$\frac{16}{81}\left(a^{6}\right)^{4}\left(b^{2}\right)^{4}\left(c^{3}\right)^{4}$$

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

$$\frac{16}{81}a^{6\times 4}b^{2\times 4}c^{3\times 4}$$

Multiply 6 times 4.

$$\frac{16}{81}a^{24}b^{2\times 4}c^{3\times 4}$$

Multiply 2 times 4.

$$\frac{16}{81}a^{24}b^{8}c^{3\times 4}$$

Multiply 3 times 4.

$$\frac{16}{81}a^{24}b^{8}c^{12}$$