Solve (-2/3a^3x^2)^4

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

Evaluate

$$\frac{16x^{8}a^{12}}{81}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{2}{3}a^{3}x^{2}\right)^{4}$$

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

$$\left(-\frac{2}{3}\right)^{4}\left(a^{3}\right)^{4}\left(x^{2}\right)^{4}$$

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

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

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

$$\frac{16}{81}a^{3\times 4}x^{2\times 4}$$

Multiply 3 times 4.

$$\frac{16}{81}a^{12}x^{2\times 4}$$

Multiply 2 times 4.

$$\frac{16}{81}a^{12}x^{8}$$

Expand

$$\frac{16x^{8}a^{12}}{81}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{2}{3}a^{3}x^{2}\right)^{4}$$

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

$$\left(-\frac{2}{3}\right)^{4}\left(a^{3}\right)^{4}\left(x^{2}\right)^{4}$$

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

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

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

$$\frac{16}{81}a^{3\times 4}x^{2\times 4}$$

Multiply 3 times 4.

$$\frac{16}{81}a^{12}x^{2\times 4}$$

Multiply 2 times 4.

$$\frac{16}{81}a^{12}x^{8}$$