Solve left(p^4q^6right)^5

$${ \left( { p }^{ 4 } { q }^{ 6 } \right) }^{ 5 }$$

Evaluate

$$p^{20}q^{30}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(p^{4}q^{6}\right)^{5}$$

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

$$\left(p^{4}\right)^{5}\left(q^{6}\right)^{5}$$

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

$$p^{4\times 5}q^{6\times 5}$$

Multiply 4 times 5.

$$p^{20}q^{6\times 5}$$

Multiply 6 times 5.

$$p^{20}q^{30}$$

Expand

$$p^{20}q^{30}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(p^{4}q^{6}\right)^{5}$$

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

$$\left(p^{4}\right)^{5}\left(q^{6}\right)^{5}$$

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

$$p^{4\times 5}q^{6\times 5}$$

Multiply 4 times 5.

$$p^{20}q^{6\times 5}$$

Multiply 6 times 5.

$$p^{20}q^{30}$$