Solve (4n^3t^2)^3

$$( 4 n ^ { 3 } t ^ { 2 } ) ^ { 3 }$$

Evaluate

$$64t^{6}n^{9}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4n^{3}t^{2}\right)^{3}$$

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

$$4^{3}\left(n^{3}\right)^{3}\left(t^{2}\right)^{3}$$

Raise 4 to the power 3.

$$64\left(n^{3}\right)^{3}\left(t^{2}\right)^{3}$$

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

$$64n^{3\times 3}t^{2\times 3}$$

Multiply 3 times 3.

$$64n^{9}t^{2\times 3}$$

Multiply 2 times 3.

$$64n^{9}t^{6}$$

Expand

$$64t^{6}n^{9}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4n^{3}t^{2}\right)^{3}$$

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

$$4^{3}\left(n^{3}\right)^{3}\left(t^{2}\right)^{3}$$

Raise 4 to the power 3.

$$64\left(n^{3}\right)^{3}\left(t^{2}\right)^{3}$$

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

$$64n^{3\times 3}t^{2\times 3}$$

Multiply 3 times 3.

$$64n^{9}t^{2\times 3}$$

Multiply 2 times 3.

$$64n^{9}t^{6}$$