Solve (2h^2k^5)^3=

$$( 2 h ^ { 2 } k ^ { 5 } ) ^ { 3 } =$$

Evaluate

$$8h^{6}k^{15}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2h^{2}k^{5}\right)^{3}$$

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

$$2^{3}\left(h^{2}\right)^{3}\left(k^{5}\right)^{3}$$

Raise 2 to the power 3.

$$8\left(h^{2}\right)^{3}\left(k^{5}\right)^{3}$$

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

$$8h^{2\times 3}k^{5\times 3}$$

Multiply 2 times 3.

$$8h^{6}k^{5\times 3}$$

Multiply 5 times 3.

$$8h^{6}k^{15}$$

Expand

$$8h^{6}k^{15}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2h^{2}k^{5}\right)^{3}$$

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

$$2^{3}\left(h^{2}\right)^{3}\left(k^{5}\right)^{3}$$

Raise 2 to the power 3.

$$8\left(h^{2}\right)^{3}\left(k^{5}\right)^{3}$$

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

$$8h^{2\times 3}k^{5\times 3}$$

Multiply 2 times 3.

$$8h^{6}k^{5\times 3}$$

Multiply 5 times 3.

$$8h^{6}k^{15}$$