steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

Recall that subtraction in exponents means the expression is a rational expression, aka fraction form.  We would have:

`(3^(4y))/(3^1)`

Then, the top, being exponents being multiplied, would be an example of (at least what we call) a "power to a power".  We can rewrite that as:

`((3^4)^y)/(3^1)`

The top becomes 81^y.   The bottom becomes 3.  So, we have:

`(81^y)/(3)`

We can't reduce anymore because of the exponent.  If that was gone, we would give 27 as the answer.  But, we have to include the exponent.  So, this would be the answer.

Educator Approved

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The expression `3^(4y-1)` cannot be solved as this is not an equation. It can be simplified.

The rules of indices that help here are:

`x^(a+b) = x^a*x^b`

`x^(a - b) = x^a/x^b`

`x^-a = 1/x^a`

`(x^a)^b = (x^b)^a = x^(a*b)`

Now applying these to `3^(4y-1)`

= `3^(4y)/3^1`

= `(3^4)^y/3`

= `81^y/3`

This cannot be simplified further.