Question

What is the quotient? PLEASE HELP QUICK

Answer 1

`\mathrm{The\:first\:option}:\quad\frac{ 1 }{ { 5 }^( 9 ) }`

Explanation:

`\frac{ { 5 }^( -6 ) }{ { 5 }^( 3 ) }`

`\mathrm{Apply\:exponent\:rule}:\quad \frac{ { x }^( a ) }{ { x }^( b ) } = { x }^( a-b )`

`= { 5 }^( -6-3 )`

`\mathrm{Subtract\:the\:numbers:}\:-6-3=-9`

`=5^(-9)`

`\mathrm{Apply\:exponent\:rule}:\quad \:{ a }^( -b ) = \frac{ 1 }{ { a }^( b ) }`

`\frac{ 1 }{ { 5 }^( 9 ) }`

So the correct answer would be:

`\mathrm{The\:first\:option}:\quad\frac{ 1 }{ { 5 }^( 9 ) }`

Answer 2

`(1)/(5^(9) )`

Explanation:

`(5^(-6) )/(5^(3) )`

Rewrite
`5^(3)` as
`5^(-6)` ×
`5^(9)`. Cancel out
`5^(-6)` in both numerator and denominator.

=
`(1)/(5^(9) )`

Hope it helps and have a great day! =D

~sunshine~