Solve (m^3n)^2(mn^5)^3

$$( m ^ { 3 } n ) ^ { 2 } ( m n ^ { 5 } ) ^ { 3 }$$

Evaluate

$$m^{9}n^{17}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(m^{3}n^{1}\right)^{2}\left(m^{1}n^{5}\right)^{3}$$

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

$$\left(m^{3}\right)^{2}\left(n^{1}\right)^{2}\left(m^{1}\right)^{3}\left(n^{5}\right)^{3}$$

Use the Commutative Property of Multiplication.

$$\left(m^{3}\right)^{2}\left(m^{1}\right)^{3}\left(n^{1}\right)^{2}\left(n^{5}\right)^{3}$$

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

$$m^{3\times 2}m^{3}n^{2}n^{5\times 3}$$

Multiply 3 times 2.

$$m^{6}m^{3}n^{2}n^{5\times 3}$$

Multiply 5 times 3.

$$m^{6}m^{3}n^{2}n^{15}$$

To multiply powers of the same base, add their exponents.

$$m^{6+3}n^{2+15}$$

Add the exponents 6 and 3.

$$m^{9}n^{2+15}$$

Add the exponents 2 and 15.

$$m^{9}n^{17}$$

Expand

$$m^{9}n^{17}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(m^{3}n^{1}\right)^{2}\left(m^{1}n^{5}\right)^{3}$$

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

$$\left(m^{3}\right)^{2}\left(n^{1}\right)^{2}\left(m^{1}\right)^{3}\left(n^{5}\right)^{3}$$

Use the Commutative Property of Multiplication.

$$\left(m^{3}\right)^{2}\left(m^{1}\right)^{3}\left(n^{1}\right)^{2}\left(n^{5}\right)^{3}$$

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

$$m^{3\times 2}m^{3}n^{2}n^{5\times 3}$$

Multiply 3 times 2.

$$m^{6}m^{3}n^{2}n^{5\times 3}$$

Multiply 5 times 3.

$$m^{6}m^{3}n^{2}n^{15}$$

To multiply powers of the same base, add their exponents.

$$m^{6+3}n^{2+15}$$

Add the exponents 6 and 3.

$$m^{9}n^{2+15}$$

Add the exponents 2 and 15.

$$m^{9}n^{17}$$