Solve d^2*(2d^5)^4

$$d ^ { 2 } \cdot ( 2 d ^ { 5 } ) ^ { 4 }$$

Evaluate

$$16d^{22}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(d^{1}\right)^{2}\times \left(2d^{5}\right)^{4}$$

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

$$1^{2}\left(d^{1}\right)^{2}\times 2^{4}\left(d^{5}\right)^{4}$$

Use the Commutative Property of Multiplication.

$$1^{2}\times 2^{4}\left(d^{1}\right)^{2}\left(d^{5}\right)^{4}$$

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

$$1^{2}\times 2^{4}d^{2}d^{5\times 4}$$

Multiply 5 times 4.

$$1^{2}\times 2^{4}d^{2}d^{20}$$

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

$$1^{2}\times 2^{4}d^{2+20}$$

Add the exponents 2 and 20.

$$1^{2}\times 2^{4}d^{22}$$

Raise 2 to the power 4.

$$16d^{22}$$

Expand

$$16d^{22}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(d^{1}\right)^{2}\times \left(2d^{5}\right)^{4}$$

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

$$1^{2}\left(d^{1}\right)^{2}\times 2^{4}\left(d^{5}\right)^{4}$$

Use the Commutative Property of Multiplication.

$$1^{2}\times 2^{4}\left(d^{1}\right)^{2}\left(d^{5}\right)^{4}$$

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

$$1^{2}\times 2^{4}d^{2}d^{5\times 4}$$

Multiply 5 times 4.

$$1^{2}\times 2^{4}d^{2}d^{20}$$

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

$$1^{2}\times 2^{4}d^{2+20}$$

Add the exponents 2 and 20.

$$1^{2}\times 2^{4}d^{22}$$

Raise 2 to the power 4.

$$16d^{22}$$