Question

Find x so that (-5)^x+1 x (-5)^5 = (-5)^7

Answer 1

x = 1

Explanation:

Using the rule of exponents

`a^(m)` ×
`a^(n)` =
`a^((m+n))` , then

`(-5)^(x+1)` ×
`(-5)^(5)` =
`(-5)^(7)`

`(-5)^((x+1+5))` =
`(-5)^(7)`

`(-5)^(x+6)` =
`(-5)^(7)`

Since bases on both sides are the same , both - 5 , then equate exponents

x + 6 = 7 ( subtract 6 from both sides )

x = 1

Answer 2

`\\ \sf\longmapsto (-5)^(x+1)* (-5)^5=(-5)^7`

`\boxed{\sf a^m* a^n=a^(mn)}`

`\\ \sf{:}\implies (-5)^(x+1+5)=(-5)^7`

`\\ \sf{:}\implies (-5)^(x+6)=(-5)^7`

`\\ \sf{:}\implies x+6=7`

`\\ \sf{:}\implies x=7-6`

`\\ \sf{:}\implies x=1`