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

$$( 4 a ^ { 3 } m ^ { 2 } ) ^ { 2 }$$

Evaluate

$$16m^{4}a^{6}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 2.

$$16\left(a^{3}\right)^{2}\left(m^{2}\right)^{2}$$

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

$$16a^{3\times 2}m^{2\times 2}$$

Multiply 3 times 2.

$$16a^{6}m^{2\times 2}$$

Multiply 2 times 2.

$$16a^{6}m^{4}$$

Expand

$$16m^{4}a^{6}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 2.

$$16\left(a^{3}\right)^{2}\left(m^{2}\right)^{2}$$

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

$$16a^{3\times 2}m^{2\times 2}$$

Multiply 3 times 2.

$$16a^{6}m^{2\times 2}$$

Multiply 2 times 2.

$$16a^{6}m^{4}$$