Solve (-2x^3)^2*(-3x^2)^3

$$( - 2 x ^ { 3 } ) ^ { 2 } \times ( - 3 x ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-108x^{12}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 3 times 2.

$$\left(-2\right)^{2}\left(-3\right)^{3}x^{6}x^{2\times 3}$$

Multiply 2 times 3.

$$\left(-2\right)^{2}\left(-3\right)^{3}x^{6}x^{6}$$

To multiply powers of the same base, add their exponents.

$$\left(-2\right)^{2}\left(-3\right)^{3}x^{6+6}$$

Add the exponents 6 and 6.

$$\left(-2\right)^{2}\left(-3\right)^{3}x^{12}$$

Raise -2 to the power 2.

$$4\left(-3\right)^{3}x^{12}$$

Raise -3 to the power 3.

$$4\left(-27\right)x^{12}$$

Multiply 4 times -27.

$$-108x^{12}$$

Expand

$$-108x^{12}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 3 times 2.

$$\left(-2\right)^{2}\left(-3\right)^{3}x^{6}x^{2\times 3}$$

Multiply 2 times 3.

$$\left(-2\right)^{2}\left(-3\right)^{3}x^{6}x^{6}$$

To multiply powers of the same base, add their exponents.

$$\left(-2\right)^{2}\left(-3\right)^{3}x^{6+6}$$

Add the exponents 6 and 6.

$$\left(-2\right)^{2}\left(-3\right)^{3}x^{12}$$

Raise -2 to the power 2.

$$4\left(-3\right)^{3}x^{12}$$

Raise -3 to the power 3.

$$4\left(-27\right)x^{12}$$

Multiply 4 times -27.

$$-108x^{12}$$