Solve k^4*(-3k^3)^2

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

Evaluate

$$9k^{10}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(k^{1}\right)^{4}\left(-3k^{3}\right)^{2}$$

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

$$1^{4}\left(k^{1}\right)^{4}\left(-3\right)^{2}\left(k^{3}\right)^{2}$$

Use the Commutative Property of Multiplication.

$$1^{4}\left(-3\right)^{2}\left(k^{1}\right)^{4}\left(k^{3}\right)^{2}$$

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

$$1^{4}\left(-3\right)^{2}k^{4}k^{3\times 2}$$

Multiply 3 times 2.

$$1^{4}\left(-3\right)^{2}k^{4}k^{6}$$

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

$$1^{4}\left(-3\right)^{2}k^{4+6}$$

Add the exponents 4 and 6.

$$1^{4}\left(-3\right)^{2}k^{10}$$

Raise -3 to the power 2.

$$9k^{10}$$

Expand

$$9k^{10}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(k^{1}\right)^{4}\left(-3k^{3}\right)^{2}$$

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

$$1^{4}\left(k^{1}\right)^{4}\left(-3\right)^{2}\left(k^{3}\right)^{2}$$

Use the Commutative Property of Multiplication.

$$1^{4}\left(-3\right)^{2}\left(k^{1}\right)^{4}\left(k^{3}\right)^{2}$$

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

$$1^{4}\left(-3\right)^{2}k^{4}k^{3\times 2}$$

Multiply 3 times 2.

$$1^{4}\left(-3\right)^{2}k^{4}k^{6}$$

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

$$1^{4}\left(-3\right)^{2}k^{4+6}$$

Add the exponents 4 and 6.

$$1^{4}\left(-3\right)^{2}k^{10}$$

Raise -3 to the power 2.

$$9k^{10}$$