Solve (3a^2)^3*a^4

$$( 3 a ^ { 2 } ) ^ { 3 } \cdot a ^ { 4 }$$

Evaluate

$$27a^{10}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(3a^{2}\right)^{3}\left(a^{1}\right)^{4}$$

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

$$3^{3}\left(a^{2}\right)^{3}\times 1^{4}\left(a^{1}\right)^{4}$$

Use the Commutative Property of Multiplication.

$$3^{3}\times 1^{4}\left(a^{2}\right)^{3}\left(a^{1}\right)^{4}$$

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

$$3^{3}\times 1^{4}a^{2\times 3}a^{4}$$

Multiply 2 times 3.

$$3^{3}\times 1^{4}a^{6}a^{4}$$

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

$$3^{3}\times 1^{4}a^{6+4}$$

Add the exponents 6 and 4.

$$3^{3}\times 1^{4}a^{10}$$

Raise 3 to the power 3.

$$27\times 1^{4}a^{10}$$

Expand

$$27a^{10}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(3a^{2}\right)^{3}\left(a^{1}\right)^{4}$$

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

$$3^{3}\left(a^{2}\right)^{3}\times 1^{4}\left(a^{1}\right)^{4}$$

Use the Commutative Property of Multiplication.

$$3^{3}\times 1^{4}\left(a^{2}\right)^{3}\left(a^{1}\right)^{4}$$

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

$$3^{3}\times 1^{4}a^{2\times 3}a^{4}$$

Multiply 2 times 3.

$$3^{3}\times 1^{4}a^{6}a^{4}$$

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

$$3^{3}\times 1^{4}a^{6+4}$$

Add the exponents 6 and 4.

$$3^{3}\times 1^{4}a^{10}$$

Raise 3 to the power 3.

$$27\times 1^{4}a^{10}$$