Question

What value of n makes the equation true?

Answer 1

The correct answer is 10.

Explanation:

If you have a product of numbers with the same base, by definition you can add the exponents.

So you have:

yⁿ2x⁹yⁿ4x²y¹⁰=8x¹¹y²⁰

Using the rule of product for x you have:

8x¹¹yⁿy¹⁰=8x¹¹y²⁰

Simplifly 8x¹¹ in both sides of the equation.

yⁿy¹⁰=y²⁰

Using the rule of product for y you have:

yⁿ⁺¹⁰=y²⁰

Divide by y on both sides:

n+10=20

Subtract 10 on both sides:

n=10

Answer 2

When multiplying exponents, they actually get added.

You can see that the x^9 and the x^2 become x^11.

This means for y to end u p at y^20, with one of them y^10, the other one would also need to be y^10.

n = 10.