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

Question

(2⋅4⋅8)a+3= (2\cdot4\cdot8)^{a+3}=

Video Solution

Solution Steps

00:10 Let's solve this problem together.
00:13 When you have a power on a product, raise each term to that power.
00:22 We'll use this rule in our exercise.
00:27 Raise each factor to the power, one step at a time.
00:32 And that's how you find the solution!

Step-by-Step Solution

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

(2⋅4⋅8)a+3=2a+34a+38a+3 (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.

Answer

2a+34a+38a+3 2^{a+3}4^{a+3}8^{a+3}

More Questions

Related Subjects

Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Exponent of a Multiplication

Question Types

Power of a Product: Variables in the exponent of the power Applying Combined Exponents Rules: Variables in the exponent of the power