Solve (x^2q)^5(x^2q)^8

$$( x ^ { 2 } q ) ^ { 5 } ( x ^ { 2 } q ) ^ { 8 }$$

Evaluate

$$q^{13}x^{26}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(x^{2}q^{1}\right)^{5}\left(x^{2}q^{1}\right)^{8}$$

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

$$\left(x^{2}\right)^{5}\left(q^{1}\right)^{5}\left(x^{2}\right)^{8}\left(q^{1}\right)^{8}$$

Use the Commutative Property of Multiplication.

$$\left(x^{2}\right)^{5}\left(x^{2}\right)^{8}\left(q^{1}\right)^{5}\left(q^{1}\right)^{8}$$

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

$$x^{2\times 5}x^{2\times 8}q^{5}q^{8}$$

Multiply 2 times 5.

$$x^{10}x^{2\times 8}q^{5}q^{8}$$

Multiply 2 times 8.

$$x^{10}x^{16}q^{5}q^{8}$$

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

$$x^{10+16}q^{5+8}$$

Add the exponents 10 and 16.

$$x^{26}q^{5+8}$$

Add the exponents 5 and 8.

$$x^{26}q^{13}$$

Expand

$$q^{13}x^{26}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(x^{2}q^{1}\right)^{5}\left(x^{2}q^{1}\right)^{8}$$

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

$$\left(x^{2}\right)^{5}\left(q^{1}\right)^{5}\left(x^{2}\right)^{8}\left(q^{1}\right)^{8}$$

Use the Commutative Property of Multiplication.

$$\left(x^{2}\right)^{5}\left(x^{2}\right)^{8}\left(q^{1}\right)^{5}\left(q^{1}\right)^{8}$$

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

$$x^{2\times 5}x^{2\times 8}q^{5}q^{8}$$

Multiply 2 times 5.

$$x^{10}x^{2\times 8}q^{5}q^{8}$$

Multiply 2 times 8.

$$x^{10}x^{16}q^{5}q^{8}$$

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

$$x^{10+16}q^{5+8}$$

Add the exponents 10 and 16.

$$x^{26}q^{5+8}$$

Add the exponents 5 and 8.

$$x^{26}q^{13}$$