Question

Part IV Questions: Answer all the questions in this part. Each problem isworth 6 points.Exercise #5:The steps to simplifying the product: 5x • 2x? The simplest terms areshown below. Write in what justifies each step.Step 1: 5x3 • 2x? = 5 • 2•x.x?Justification:Step 2: 5•2•x •x? = (5 • 2) : (x} . x) Justify:Step 3: (5.2) (x3 • x?) = 10x10Justify

Answer 1

We are given the following expression

`5x^3\cdot2x^7`

We are asked to provide justification on how it is being simplified.

Step 1: Justification

Since the base is the same (x) the coefficients are multiplied together.

`mx^a\cdot nx^b=m\cdot n\cdot x^a\cdot x^b`

Step 2: Justification

Combining the like terms together

`m\cdot n\cdot x^a\cdot x^b=(m\cdot n)\cdot(x^a\cdot x^b)`

Step 3: Justification

Apply the exponent's rule (since the base is the same their powers can be added)

`x^a\cdot x^b=x^(a+b)`