Question

How do you simplify `-1^15`?

Answer 1

The answer is -1

Explanation:

`-1^-15`

is (-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1) = -1

When the exponent of a negative root is odd the negative will multiply to a negative solution.

Answer 2

`-1`

Explanation:

Given:`" " (-1)^15`

`color(blue)("Consider the index (powers)")`

`"Known that: "(-1)^2=+1`

But `->15/2 =7 +" Remainder of 1"`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Using this to solve your problem")`

Split your question:

`(-1)^14xx(-1)`

`color(brown)("'---------------Something to consider----------------------------")`

`color(brown)("Think for a moment about ")`

`color(brown)((-1)xx(-1)xx(-1)xx(-1)xx(-1)xx(-1))`

`color(brown)("This is the same as "(-1)^2xx(-1)^2xx(-1)^2)`

`color(brown)("Which is the same as " "((-1)^2)^3)`
`color(brown)("Observe that the outermost index of 3 is "1/2" the original count. Also notice that "2xx3=6)`
`color(brown)("'---------------------------------------------------------------------------")`

`" " ((-1)^2)^7xx"Remainder"" "->" "(+1)^7xx"Remainder"`

So we have`" "(+1)^7xx(-1)=-1`

`color(green)("If an index is odd, then the final value is negative")`
`color(green)("If an index is even then the final value is positive")`

Answer 3

`-1`

Explanation:

As there are no parentheses around the `-1`, you need to evaluate this expression in the following order:

1) first compute the power: `1^15 = 1`

2) afterwards negate the result from above: `-(1) = -1`.

Thus, you need to compute:

`- 1^15 = - (1^15) = - (1) = -1`