The question says we are to check the options that are equal
[tex]\frac{7^6}{7^3}[/tex]
Using the law of indices
[tex]\frac{7^6}{7^3}=7^{6-3\text{ }}=7^3[/tex]
So we will check all the options(applying the laws of indices)
The first option is
[tex]7^9(7^{-6})=7^{9-6}=7^3[/tex]
yes, the first option is equivalent
We will move on and check the second option
[tex]\frac{7^{-8}}{7^{-11}}\text{ = }7^{-8+11}=7^3[/tex]
Yes the second option is equivalent
We will move on to check the third option
[tex](7^5)(7^3)divideby7^{4\text{ }}=7^{5+3-4\text{ }}=7^4[/tex]
No the third option is not eqquivalent to the question
We will move to tthe next option, fourth option
[tex]7^{-3\text{ }}\times7^{6\text{ }}=7^{-3+6}=7^3[/tex]
yes this option is equivalent to the fraction
Moving on to the fifth option
[tex](7^3)^{0\text{ }}=7^{3\times0}=7^0=\text{ 1}[/tex]
No the fifth option is not equivalent to the question
