Solve (2×4×8)^(a+3): Understanding Compound Power Expressions

Let's begin by using the distributing exponents rule (An exponent outside of a parentheses needs to be distributed across all the numbers and variables within the parentheses)

$(x\cdot y)^n=x^n\cdot y^n$We first apply this rule to the given problem:

$(2\cdot4\cdot8)^{a+3}= 2^{a+3}4^{a+3}8^{a+3}$When then we apply the power to each of the terms of the product inside the parentheses separately and maintain the multiplication.

The correct answer is option d.