Solve (-5x^2y^3)^2

$$( - 5 x ^ { 2 } y ^ { 3 } ) ^ { 2 }$$

Evaluate

$$25x^{4}y^{6}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-5x^{2}y^{3}\right)^{2}$$

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

$$\left(-5\right)^{2}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}$$

Raise -5 to the power 2.

$$25\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}$$

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

$$25x^{2\times 2}y^{3\times 2}$$

Multiply 2 times 2.

$$25x^{4}y^{3\times 2}$$

Multiply 3 times 2.

$$25x^{4}y^{6}$$

Expand

$$25x^{4}y^{6}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-5x^{2}y^{3}\right)^{2}$$

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

$$\left(-5\right)^{2}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}$$

Raise -5 to the power 2.

$$25\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}$$

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

$$25x^{2\times 2}y^{3\times 2}$$

Multiply 2 times 2.

$$25x^{4}y^{3\times 2}$$

Multiply 3 times 2.

$$25x^{4}y^{6}$$