Answer: [tex]x=-1[/tex]
Step-by-step explanation:
By the negative exponent rule, you have that:
[tex](\frac{1}{a})^n=a^{-n}[/tex]
By the exponents properties, you know that:
[tex](m^n)^l=m^{(nl)}[/tex]
Therefore, you can rewrite the left side of the equation has following:
[tex](\frac{1}{8})^{-(2x+7)}=(\frac{1}{32})^{3x}[/tex]
 Descompose 32 and 8 into its prime factors:
[tex]32=2*2*2*2*2=2^5\\8=2*2*2=2^3[/tex]
Rewrite:
[tex](\frac{1}{2^3})^{-(2x+7)}=(\frac{1}{2^5})^{3x}[/tex]
Then:
[tex](\frac{1}{2})^{-3(2x+7)}=(\frac{1}{2})^{5(3x)}[/tex]
As the base are equal, then:
[tex]-3(2x+7)=5(3x)[/tex]
Solve for x:
[tex]-6x-21=15x\\-21=15x+6x\\-21=21x\\x=-1[/tex]
