Respuesta :

[tex]\\ \sf\longmapsto (-5)^{x+1}\times (-5)^5=(-5)^7[/tex]

[tex]\boxed{\sf a^m\times a^n=a^{mn}}[/tex]

[tex]\\ \sf{:}\implies (-5)^{x+1+5}=(-5)^7[/tex]

[tex]\\ \sf{:}\implies (-5)^{x+6}=(-5)^7[/tex]

[tex]\\ \sf{:}\implies x+6=7[/tex]

[tex]\\ \sf{:}\implies x=7-6[/tex]

[tex]\\ \sf{:}\implies x=1[/tex]

Answer:

x = 1

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then

[tex](-5)^{x+1}[/tex] × [tex](-5)^{5}[/tex] = [tex](-5)^{7}[/tex]

[tex](-5)^{(x+1+5)}[/tex] = [tex](-5)^{7}[/tex]

[tex](-5)^{x+6}[/tex] = [tex](-5)^{7}[/tex]

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

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

x = 1

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