Answer:
B. [tex]5^3+x[/tex]
D. [tex]125.5^x[/tex]
Step-by-step explanation:
Given expression is,
[tex]5^3.5^x[/tex]
[tex]=125.5^x[/tex]
In option A,
[tex]5^{3x}=(5^3)^x=125^x[/tex] ( [tex](a^m)^n=a^{mn}[/tex] )
In option B,
[tex]5^{3+x}=5^3.5^x=125.5^x[/tex] ( [tex]a^{m+n}=a^m.a^n[/tex] )
In option C,
[tex]25^3x=15625x[/tex]
In option D,
[tex]125.5^x[/tex]
In option E,
[tex](5x)^3=5^3.x^3=125x^3[/tex] ( [tex](ab)^m=a^m.b^m[/tex] )
In option F,
[tex]5^{3-x}=\frac{5^3}{5^x}=\frac{125}{5^x}[/tex] ( [tex]a^{m-n}=\frac{a^m}{a^n}[/tex] )
Hence, by the above explanation it is clear that option B and option D are equivalent to the given expression.
