Solve (k^2*2m^5)^6=

$$( k ^ { 2 } \times 2 m ^ { 5 } ) ^ { 6 } =$$

Evaluate

$$64k^{12}m^{30}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2k^{2}m^{5}\right)^{6}$$

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

$$2^{6}\left(k^{2}\right)^{6}\left(m^{5}\right)^{6}$$

Raise 2 to the power 6.

$$64\left(k^{2}\right)^{6}\left(m^{5}\right)^{6}$$

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

$$64k^{2\times 6}m^{5\times 6}$$

Multiply 2 times 6.

$$64k^{12}m^{5\times 6}$$

Multiply 5 times 6.

$$64k^{12}m^{30}$$

Expand

$$64k^{12}m^{30}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2k^{2}m^{5}\right)^{6}$$

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

$$2^{6}\left(k^{2}\right)^{6}\left(m^{5}\right)^{6}$$

Raise 2 to the power 6.

$$64\left(k^{2}\right)^{6}\left(m^{5}\right)^{6}$$

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

$$64k^{2\times 6}m^{5\times 6}$$

Multiply 2 times 6.

$$64k^{12}m^{5\times 6}$$

Multiply 5 times 6.

$$64k^{12}m^{30}$$