Answer:
Because the bases are equal, the exponents must also be equal
Step-by-step explanation:
I just had this question on E2020
The word in blank a will be " base" and word in blank b will be "exponents" so we can choose option a and b as our options from the given choices.
so the complete sentence will be as given below
Because the base are equal , the exponents must also be equal.
Given algebraic equation is written as follows
[tex]\rm 8 ^ {x-4} = 8^{10}[/tex]
We are given a statement that is to be completed
The given statement is written as below
" Because the (blank a) are equal , the (blank b) must also be equal."
We have to fill in the correct choices options from the given options
According to the property of the exponents we can write
[tex]\rm B^n = B^m........(1) \\n = m \\B = Base\; of \; the\; exponent\\n , m = Exponents \\[/tex]
According to equation (1) we can conclude that if the bases are equal the exponents must equal.
in the given expression
Base = 8
Both terms of left hand side and the right hand side have base which is 8
so according to the property explained in equation (1) we can say conclude that both the exponents in the given expression are equal so we can write
[tex]\rm x-4 =10\\x =10 + 4\\x = 14[/tex]
So we an conclude that word in blank a will be " base" and word in blank b will be "exponents" so we can choose option a and b as our options from the given choices.
so the complete sentence will be as given below
Because the base are equal , the exponents must also be equal.
For more information please refer to the link given below
https://brainly.com/question/5497425
