Solve (-2/3a^2b)^3=

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

Evaluate

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

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

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

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

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

Multiply 2 times 3.

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

Expand

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

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

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

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

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

Multiply 2 times 3.

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