Prove the Equation: x*xxxx*x is Equal to 2 x — Easy Explanation for Students

Algebra is kind of tricky and tough? No it’s all about fun guys. The most irritating and problematic thing is to prove some algebra equations right? Here I am helping you to simplify and prove a algebra equation = “x*xxxx*x is equal to 2 x” or “x*xxxx*x = 2”. But is this really true?

Let’s find out to prove that it is true. Let me help you.

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Prove the Equation = x*xxxx*x is Equal to 2 x

Many students get confused when they see an expression like:

x × xxxx × x

and then someone says it is equal to:

2x

At first it looks impossible—but when we break it into small steps, it becomes very easy to understand.
Let’s learn this in the simplest way!

Step 1: Meaning of “xxxx”

When we write xxxx, it simply means:

x written 4 times

That is:

xxxx = x × x × x × x = x⁴

So the expression becomes:

x × xxxx × x = x × x⁴ × x

Step 2: Combine all x’s together

In mathematics, when we multiply powers with the same base, we add the exponents:

xᵃ × xᵇ = xᵃ⁺ᵇ

So here:

  • first x = x¹
  • xxxx = x⁴
  • last x = x¹

Now add all exponents:

x¹ × x⁴ × x¹ = x⁶

So the expression simplifies to:

✅ x × xxxx × x = x⁶

This is the correct simplified form.

Step 3: When does x⁶ become equal to 2x?

Now if someone says:

x × xxxx × x = 2x

That means:

x⁶ = 2x

Let’s solve this.

Divide both sides by x (as long as x ≠ 0):

x⁵ = 2

Now take the 5th root of both sides:

👉 x = √[5]{2} (the 5th root of 2)

This is the value of x that makes the equation true.

x*xxxx*x is equal to 2 x
x*xxxx*x is equal to 2 x

Final Result

ExpressionSimplified Form
x × xxxx × xx⁶
x × xxxx × x = 2xPossible only when x = √[5]{2}

Easy Proof for Students

Let x = √[5]{2}

Then:

x⁶
= (√[5]{2})⁶
= 2 × √[5]{2}
= 2x

So the statement is true!

Why is this important for students?

✔ Helps understand multiplication of repeated terms
✔ Teaches how to convert repeated letters into exponents
✔ Shows how to simplify expressions using power rules
✔ Gives confidence in solving equations with exponents

This example is great for practicing exponent laws, simplification, and solving equations.

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