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

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

Evaluate

$$27a^{7}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

$$\left(a^{2}\right)^{2}\times 3^{3}\left(a^{1}\right)^{3}$$

Use the Commutative Property of Multiplication.

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

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

$$3^{3}a^{2\times 2}a^{3}$$

Multiply 2 times 2.

$$3^{3}a^{4}a^{3}$$

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

$$3^{3}a^{4+3}$$

Add the exponents 4 and 3.

$$3^{3}a^{7}$$

Raise 3 to the power 3.

$$27a^{7}$$

Expand

$$27a^{7}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

$$\left(a^{2}\right)^{2}\times 3^{3}\left(a^{1}\right)^{3}$$

Use the Commutative Property of Multiplication.

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

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

$$3^{3}a^{2\times 2}a^{3}$$

Multiply 2 times 2.

$$3^{3}a^{4}a^{3}$$

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

$$3^{3}a^{4+3}$$

Add the exponents 4 and 3.

$$3^{3}a^{7}$$

Raise 3 to the power 3.

$$27a^{7}$$