Simplify the Expression: a³ · a² · b⁴ · b⁵ Using Exponent Rules

Simplify the expression:

a3⋅a2⋅b4⋅b5= a^3\cdot a^2\cdot b^4\cdot b^5=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:10 Alright, let's simplify this together.
00:13 We'll use the formula for multiplying powers. Here's how it works:
00:18 When you multiply a number, A, raised to the M, with the same number, A, raised to the N,
00:24 it equals the number, A, raised to the power of M plus N.
00:30 Let's apply this rule to our problem!
00:33 We'll combine the powers with the same base. And there you go!

Step-by-step written solution

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1

Understand the problem

Simplify the expression:

a3⋅a2⋅b4⋅b5= a^3\cdot a^2\cdot b^4\cdot b^5=

2

Step-by-step solution

In the exercise of multiplying powers, we will add up all the powers of the same product, in this case the terms a, b

We use the formula:

an×am=an+m a^n\times a^m=a^{n+m}

We are going to focus on the term a:

a3×a2=a3+2=a5 a^3\times a^2=a^{3+2}=a^5

We are going to focus on the term b:

b4×b5=b4+5=b9 b^4\times b^5=b^{4+5}=b^9

Therefore, the exercise that will be obtained after simplification is:

a5×b9 a^5\times b^9

3

Final Answer

a5⋅b9 a^5\cdot b^9

Practice Quiz

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\( 112^0=\text{?} \)

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