Question

What value of n makes the equation true? Show your work.
(-4)¹⁰ / (-4)ⁿ =(-4)² . (-4)²

Answer 1

We can start by simplifying the expression on the left side:

(-4)¹⁰ / (-4)ⁿ = (-4)⁹ * (-4) / (-4)ⁿ

Then, we can simplify the expression on the right side:

(-4)⁹ * (-4) / (-4)ⁿ = (-4)⁹ / (-4)ⁿ * (-4)

Now, we can set the two expressions equal to each other:

(-4)⁹ / (-4)ⁿ = (-4)⁹ / (-4)ⁿ * (-4)

Dividing both sides by (-4)⁹ gives us:

1 / (-4)ⁿ = (-4)

Multiplying both sides by -4 gives us:

-4 / (-4)ⁿ = (-4) * (-4)

Simplifying the right side gives us:

-4 / (-4)ⁿ = 16

Dividing both sides by -4 gives us:

1 / (-4)ⁿ = -4

Then, we can solve for n by taking the reciprocal of both sides:

(-4)ⁿ = -4

n = 1

So the value of n that makes the equation true is 1.