Solve (r^9*m^8)^5(r*m)^5

$$( r ^ { 9 } \cdot m ^ { 8 } ) ^ { 5 } ( r \cdot m ) ^ { 5 }$$

Evaluate

$$m^{45}r^{50}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(r^{9}m^{8}\right)^{5}\left(r^{1}m^{1}\right)^{5}$$

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

$$\left(r^{9}\right)^{5}\left(m^{8}\right)^{5}\left(r^{1}\right)^{5}\left(m^{1}\right)^{5}$$

Use the Commutative Property of Multiplication.

$$\left(r^{9}\right)^{5}\left(r^{1}\right)^{5}\left(m^{8}\right)^{5}\left(m^{1}\right)^{5}$$

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

$$r^{9\times 5}r^{5}m^{8\times 5}m^{5}$$

Multiply 9 times 5.

$$r^{45}r^{5}m^{8\times 5}m^{5}$$

Multiply 8 times 5.

$$r^{45}r^{5}m^{40}m^{5}$$

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

$$r^{45+5}m^{40+5}$$

Add the exponents 45 and 5.

$$r^{50}m^{40+5}$$

Add the exponents 40 and 5.

$$r^{50}m^{45}$$

Expand

$$m^{45}r^{50}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(r^{9}m^{8}\right)^{5}\left(r^{1}m^{1}\right)^{5}$$

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

$$\left(r^{9}\right)^{5}\left(m^{8}\right)^{5}\left(r^{1}\right)^{5}\left(m^{1}\right)^{5}$$

Use the Commutative Property of Multiplication.

$$\left(r^{9}\right)^{5}\left(r^{1}\right)^{5}\left(m^{8}\right)^{5}\left(m^{1}\right)^{5}$$

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

$$r^{9\times 5}r^{5}m^{8\times 5}m^{5}$$

Multiply 9 times 5.

$$r^{45}r^{5}m^{8\times 5}m^{5}$$

Multiply 8 times 5.

$$r^{45}r^{5}m^{40}m^{5}$$

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

$$r^{45+5}m^{40+5}$$

Add the exponents 45 and 5.

$$r^{50}m^{40+5}$$

Add the exponents 40 and 5.

$$r^{50}m^{45}$$