Answer:
x = -11
Step-by-step explanation:
Convert fraction into negative exponential form: [tex](36^-^1)^x^-^4=(216^-^1)^x^+^1\\[/tex]
Simplify using exponent power rule: [tex](a^n)^m=a^n^m:36^-^x^+^4=216^-^x^-^1[/tex]
Convert both sides of the equation into terms with same base:[tex](6^2)^-^x^+^4=(6^3)^-^x^-^1[/tex]
Simplify using exponent power rule:
[tex](a^n)^m=a^n^m:6^-^2^x^+^8=6^-^3^x^-^3[/tex]
Based on the given conditions, corresponding exponents are equal:
[tex]-2x=8=-3x-3[/tex]
Rearrange unknown terms to the left side of the equation:
[tex]-2x+3x=-3-8[/tex]
Combine like terms: [tex]x=-3-8[/tex]
Calculate the sum or difference: [tex]x = -11[/tex]
Thurs, x = -11
[RevyBreeze]
