Solve (-5x^4y^4)^3

$$( - 5 x ^ { 4 } y ^ { 4 } ) ^ { 3 }$$

Evaluate

$$-125\left(xy\right)^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-5x^{4}y^{4}\right)^{3}$$

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

$$\left(-5\right)^{3}\left(x^{4}\right)^{3}\left(y^{4}\right)^{3}$$

Raise -5 to the power 3.

$$-125\left(x^{4}\right)^{3}\left(y^{4}\right)^{3}$$

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

$$-125x^{4\times 3}y^{4\times 3}$$

Multiply 4 times 3.

$$-125x^{12}y^{4\times 3}$$

Multiply 4 times 3.

$$-125x^{12}y^{12}$$

Expand

$$-125\left(xy\right)^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-5x^{4}y^{4}\right)^{3}$$

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

$$\left(-5\right)^{3}\left(x^{4}\right)^{3}\left(y^{4}\right)^{3}$$

Raise -5 to the power 3.

$$-125\left(x^{4}\right)^{3}\left(y^{4}\right)^{3}$$

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

$$-125x^{4\times 3}y^{4\times 3}$$

Multiply 4 times 3.

$$-125x^{12}y^{4\times 3}$$

Multiply 4 times 3.

$$-125x^{12}y^{12}$$