Solve left(3a^2x^4right)^3

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

Evaluate

$$27a^{6}x^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power 3.

$$27\left(a^{2}\right)^{3}\left(x^{4}\right)^{3}$$

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

$$27a^{2\times 3}x^{4\times 3}$$

Multiply 2 times 3.

$$27a^{6}x^{4\times 3}$$

Multiply 4 times 3.

$$27a^{6}x^{12}$$

Expand

$$27a^{6}x^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power 3.

$$27\left(a^{2}\right)^{3}\left(x^{4}\right)^{3}$$

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

$$27a^{2\times 3}x^{4\times 3}$$

Multiply 2 times 3.

$$27a^{6}x^{4\times 3}$$

Multiply 4 times 3.

$$27a^{6}x^{12}$$