Solve (2b^2)^3*(3b^4)^2

$$( 2 b ^ { 2 } ) ^ { 3 } \times ( 3 b ^ { 4 } ) ^ { 2 }$$

Evaluate

$$72b^{14}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2b^{2}\right)^{3}\times \left(3b^{4}\right)^{2}$$

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

$$2^{3}\left(b^{2}\right)^{3}\times 3^{2}\left(b^{4}\right)^{2}$$

Use the Commutative Property of Multiplication.

$$2^{3}\times 3^{2}\left(b^{2}\right)^{3}\left(b^{4}\right)^{2}$$

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

$$2^{3}\times 3^{2}b^{2\times 3}b^{4\times 2}$$

Multiply 2 times 3.

$$2^{3}\times 3^{2}b^{6}b^{4\times 2}$$

Multiply 4 times 2.

$$2^{3}\times 3^{2}b^{6}b^{8}$$

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

$$2^{3}\times 3^{2}b^{6+8}$$

Add the exponents 6 and 8.

$$2^{3}\times 3^{2}b^{14}$$

Raise 2 to the power 3.

$$8\times 3^{2}b^{14}$$

Raise 3 to the power 2.

$$8\times 9b^{14}$$

Multiply 8 times 9.

$$72b^{14}$$

Expand

$$72b^{14}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2b^{2}\right)^{3}\times \left(3b^{4}\right)^{2}$$

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

$$2^{3}\left(b^{2}\right)^{3}\times 3^{2}\left(b^{4}\right)^{2}$$

Use the Commutative Property of Multiplication.

$$2^{3}\times 3^{2}\left(b^{2}\right)^{3}\left(b^{4}\right)^{2}$$

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

$$2^{3}\times 3^{2}b^{2\times 3}b^{4\times 2}$$

Multiply 2 times 3.

$$2^{3}\times 3^{2}b^{6}b^{4\times 2}$$

Multiply 4 times 2.

$$2^{3}\times 3^{2}b^{6}b^{8}$$

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

$$2^{3}\times 3^{2}b^{6+8}$$

Add the exponents 6 and 8.

$$2^{3}\times 3^{2}b^{14}$$

Raise 2 to the power 3.

$$8\times 3^{2}b^{14}$$

Raise 3 to the power 2.

$$8\times 9b^{14}$$

Multiply 8 times 9.

$$72b^{14}$$