Solve (4x^3y^6z^8)^3

$$( 4 x ^ { 3 } y ^ { 6 } z ^ { 8 } ) ^ { 3 }$$

Evaluate

$$64x^{9}y^{18}z^{24}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(4x^{3}y^{6}z^{8}\right)^{3}$$

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

$$4^{3}\left(x^{3}\right)^{3}\left(y^{6}\right)^{3}\left(z^{8}\right)^{3}$$

Raise 4 to the power 3.

$$64\left(x^{3}\right)^{3}\left(y^{6}\right)^{3}\left(z^{8}\right)^{3}$$

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

$$64x^{3\times 3}y^{6\times 3}z^{8\times 3}$$

Multiply 3 times 3.

$$64x^{9}y^{6\times 3}z^{8\times 3}$$

Multiply 6 times 3.

$$64x^{9}y^{18}z^{8\times 3}$$

Multiply 8 times 3.

$$64x^{9}y^{18}z^{24}$$

Expand

$$64x^{9}y^{18}z^{24}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(4x^{3}y^{6}z^{8}\right)^{3}$$

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

$$4^{3}\left(x^{3}\right)^{3}\left(y^{6}\right)^{3}\left(z^{8}\right)^{3}$$

Raise 4 to the power 3.

$$64\left(x^{3}\right)^{3}\left(y^{6}\right)^{3}\left(z^{8}\right)^{3}$$

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

$$64x^{3\times 3}y^{6\times 3}z^{8\times 3}$$

Multiply 3 times 3.

$$64x^{9}y^{6\times 3}z^{8\times 3}$$

Multiply 6 times 3.

$$64x^{9}y^{18}z^{8\times 3}$$

Multiply 8 times 3.

$$64x^{9}y^{18}z^{24}$$