Solve (nm^4)^4*(mn)^4

$$( n m ^ { 4 } ) ^ { 4 } \cdot ( m n ) ^ { 4 }$$

Evaluate

$$n^{8}m^{20}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(n^{1}m^{4}\right)^{4}\left(n^{1}m^{1}\right)^{4}$$

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

$$\left(n^{1}\right)^{4}\left(m^{4}\right)^{4}\left(n^{1}\right)^{4}\left(m^{1}\right)^{4}$$

Use the Commutative Property of Multiplication.

$$\left(n^{1}\right)^{4}\left(n^{1}\right)^{4}\left(m^{4}\right)^{4}\left(m^{1}\right)^{4}$$

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

$$n^{4}n^{4}m^{4\times 4}m^{4}$$

Multiply 4 times 4.

$$n^{4}n^{4}m^{16}m^{4}$$

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

$$n^{4+4}m^{16+4}$$

Add the exponents 4 and 4.

$$n^{8}m^{16+4}$$

Add the exponents 16 and 4.

$$n^{8}m^{20}$$

Expand

$$n^{8}m^{20}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(n^{1}m^{4}\right)^{4}\left(n^{1}m^{1}\right)^{4}$$

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

$$\left(n^{1}\right)^{4}\left(m^{4}\right)^{4}\left(n^{1}\right)^{4}\left(m^{1}\right)^{4}$$

Use the Commutative Property of Multiplication.

$$\left(n^{1}\right)^{4}\left(n^{1}\right)^{4}\left(m^{4}\right)^{4}\left(m^{1}\right)^{4}$$

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

$$n^{4}n^{4}m^{4\times 4}m^{4}$$

Multiply 4 times 4.

$$n^{4}n^{4}m^{16}m^{4}$$

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

$$n^{4+4}m^{16+4}$$

Add the exponents 4 and 4.

$$n^{8}m^{16+4}$$

Add the exponents 16 and 4.

$$n^{8}m^{20}$$