Solve (3x^3)^2(3x^5)^3

$$( 3 x ^ { 3 } ) ^ { 2 } ( 3 x ^ { 5 } ) ^ { 3 }$$

Evaluate

$$243x^{21}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(3x^{3}\right)^{2}\times \left(3x^{5}\right)^{3}$$

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

$$3^{2}\left(x^{3}\right)^{2}\times 3^{3}\left(x^{5}\right)^{3}$$

Use the Commutative Property of Multiplication.

$$3^{2}\times 3^{3}\left(x^{3}\right)^{2}\left(x^{5}\right)^{3}$$

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

$$3^{2}\times 3^{3}x^{3\times 2}x^{5\times 3}$$

Multiply 3 times 2.

$$3^{2}\times 3^{3}x^{6}x^{5\times 3}$$

Multiply 5 times 3.

$$3^{2}\times 3^{3}x^{6}x^{15}$$

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

$$3^{2}\times 3^{3}x^{6+15}$$

Add the exponents 6 and 15.

$$3^{2}\times 3^{3}x^{21}$$

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

$$3^{2+3}x^{21}$$

Add the exponents 2 and 3.

$$3^{5}x^{21}$$

Expand

$$243x^{21}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(3x^{3}\right)^{2}\times \left(3x^{5}\right)^{3}$$

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

$$3^{2}\left(x^{3}\right)^{2}\times 3^{3}\left(x^{5}\right)^{3}$$

Use the Commutative Property of Multiplication.

$$3^{2}\times 3^{3}\left(x^{3}\right)^{2}\left(x^{5}\right)^{3}$$

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

$$3^{2}\times 3^{3}x^{3\times 2}x^{5\times 3}$$

Multiply 3 times 2.

$$3^{2}\times 3^{3}x^{6}x^{5\times 3}$$

Multiply 5 times 3.

$$3^{2}\times 3^{3}x^{6}x^{15}$$

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

$$3^{2}\times 3^{3}x^{6+15}$$

Add the exponents 6 and 15.

$$3^{2}\times 3^{3}x^{21}$$

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

$$3^{2+3}x^{21}$$

Add the exponents 2 and 3.

$$3^{5}x^{21}$$