Solve (st)^6(s^6t)^2

$$( s t ) ^ { 6 } ( s ^ { 6 } t ) ^ { 2 }$$

Evaluate

$$t^{8}s^{18}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(s^{1}t^{1}\right)^{6}\left(s^{6}t^{1}\right)^{2}$$

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

$$\left(s^{1}\right)^{6}\left(t^{1}\right)^{6}\left(s^{6}\right)^{2}\left(t^{1}\right)^{2}$$

Use the Commutative Property of Multiplication.

$$\left(s^{1}\right)^{6}\left(s^{6}\right)^{2}\left(t^{1}\right)^{6}\left(t^{1}\right)^{2}$$

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

$$s^{6}s^{6\times 2}t^{6}t^{2}$$

Multiply 6 times 2.

$$s^{6}s^{12}t^{6}t^{2}$$

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

$$s^{6+12}t^{6+2}$$

Add the exponents 6 and 12.

$$s^{18}t^{6+2}$$

Add the exponents 6 and 2.

$$s^{18}t^{8}$$

Expand

$$t^{8}s^{18}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(s^{1}t^{1}\right)^{6}\left(s^{6}t^{1}\right)^{2}$$

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

$$\left(s^{1}\right)^{6}\left(t^{1}\right)^{6}\left(s^{6}\right)^{2}\left(t^{1}\right)^{2}$$

Use the Commutative Property of Multiplication.

$$\left(s^{1}\right)^{6}\left(s^{6}\right)^{2}\left(t^{1}\right)^{6}\left(t^{1}\right)^{2}$$

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

$$s^{6}s^{6\times 2}t^{6}t^{2}$$

Multiply 6 times 2.

$$s^{6}s^{12}t^{6}t^{2}$$

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

$$s^{6+12}t^{6+2}$$

Add the exponents 6 and 12.

$$s^{18}t^{6+2}$$

Add the exponents 6 and 2.

$$s^{18}t^{8}$$