Solve (2s^3)^6*(2s^4)^-2

$$( 2 s ^ { 3 } ) ^ { 6 } \times ( 2 s ^ { 4 } ) ^ { - 2 }$$

Evaluate

$$16s^{10}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2s^{3}\right)^{6}\times \left(2s^{4}\right)^{-2}$$

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

$$2^{6}\left(s^{3}\right)^{6}\times 2^{-2}\left(s^{4}\right)^{-2}$$

Use the Commutative Property of Multiplication.

$$2^{6}\times 2^{-2}\left(s^{3}\right)^{6}\left(s^{4}\right)^{-2}$$

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

$$2^{6}\times 2^{-2}s^{3\times 6}s^{4\left(-2\right)}$$

Multiply 3 times 6.

$$2^{6}\times 2^{-2}s^{18}s^{4\left(-2\right)}$$

Multiply 4 times -2.

$$2^{6}\times 2^{-2}s^{18}s^{-8}$$

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

$$2^{6}\times 2^{-2}s^{18-8}$$

Add the exponents 18 and -8.

$$2^{6}\times 2^{-2}s^{10}$$

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

$$2^{6-2}s^{10}$$

Add the exponents 6 and -2.

$$2^{4}s^{10}$$

Expand

$$16s^{10}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2s^{3}\right)^{6}\times \left(2s^{4}\right)^{-2}$$

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

$$2^{6}\left(s^{3}\right)^{6}\times 2^{-2}\left(s^{4}\right)^{-2}$$

Use the Commutative Property of Multiplication.

$$2^{6}\times 2^{-2}\left(s^{3}\right)^{6}\left(s^{4}\right)^{-2}$$

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

$$2^{6}\times 2^{-2}s^{3\times 6}s^{4\left(-2\right)}$$

Multiply 3 times 6.

$$2^{6}\times 2^{-2}s^{18}s^{4\left(-2\right)}$$

Multiply 4 times -2.

$$2^{6}\times 2^{-2}s^{18}s^{-8}$$

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

$$2^{6}\times 2^{-2}s^{18-8}$$

Add the exponents 18 and -8.

$$2^{6}\times 2^{-2}s^{10}$$

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

$$2^{6-2}s^{10}$$

Add the exponents 6 and -2.

$$2^{4}s^{10}$$