How do you simplify #-1^15#?

3 Answers
Feb 12, 2016

Answer:

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.

Feb 12, 2016

Answer:

#-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")#

Feb 12, 2016

Answer:

#-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#