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

$$( - a ^ { 2 } ) ^ { 2 } \cdot ( - 2 a ^ { 3 } ) ^ { 2 }$$

Evaluate

$$4a^{10}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times 2.

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

Multiply 3 times 2.

$$\left(-2\right)^{2}a^{4}a^{6}$$

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

$$\left(-2\right)^{2}a^{4+6}$$

Add the exponents 4 and 6.

$$\left(-2\right)^{2}a^{10}$$

Raise -2 to the power 2.

$$4a^{10}$$

Expand

$$4a^{10}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times 2.

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

Multiply 3 times 2.

$$\left(-2\right)^{2}a^{4}a^{6}$$

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

$$\left(-2\right)^{2}a^{4+6}$$

Add the exponents 4 and 6.

$$\left(-2\right)^{2}a^{10}$$

Raise -2 to the power 2.

$$4a^{10}$$