Which expressions are equivalent to 17^5÷(17^6)(17^−3)/17^−2?
Select all that are correct.
a.1/5^0
b.1/17^1
c.(−1)^5
d.17^1
e.(−1)^2
as written, none of them.
17^5÷(17^6)(17^−3)/17^−2 = 1/17^2
17^5÷((17^6)(17^−3)/17^−2) = 1
so, (a) or (e)
Put in some other parentheses and you might get other answers.
To find equivalent expressions for 17^5 ÷ (17^6)(17^-3) / 17^-2, we can simplify the expression step by step.
First, let's simplify 17^5 ÷ (17^6)(17^-3). When we divide two numbers with the same base, we subtract the exponents:
17^5 ÷ (17^6)(17^-3) = 17^(5 - 6 - (-3)) = 17^-4.
Next, we divide by 17^-2. When we divide two numbers with the same base, we subtract the exponents:
17^-4 ÷ 17^-2 = 17^(-4 - (-2)) = 17^-2.
So, the equivalent expression is 17^-2.
Now let's check the options to see which one(s) are equivalent to 17^-2:
a. 1/5^0: 5^0 equals 1, so this expression is equivalent to 1/1, which is 1. It is not equivalent to 17^-2.
b. 1/17^1: 17^1 equals 17, so this expression is equivalent to 1/17. It is not equivalent to 17^-2.
c. (-1)^5: (-1)^5 equals -1. It is not equivalent to 17^-2.
d. 17^1: 17^1 equals 17. It is not equivalent to 17^-2.
e. (-1)^2: (-1)^2 equals 1. It is not equivalent to 17^-2.
Therefore, the correct answer is none of the above. None of the provided expressions are equivalent to 17^-2.