Can someone please help me evaluate this equation its in the topic indices  `3^(4y-1)`

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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.

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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.

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