Apply the Properties of Integer Exponents to generate equivalent expressions to 37⋅3−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
37⋅3−9=
Using the properties of integer exponents, we can rewrite 37 as 3 and rewrite 3^(-9) as 1/(3^9).
Therefore, 37⋅3^(-9) is equivalent to 3⋅1/(3^9).
Simplifying further, we have 3/(3^9).
Using the property of exponents that states a^(-n) = 1/(a^n), we can rewrite 3^9 as (3^9)^(-1), which is equal to 1/(3^(9*1)).
Therefore, 3/(3^9) is equivalent to 3/(3^(9*1)).
Using the property of exponents that states a^(mn) = (a^m)^n, we can rewrite 3^(9*1) as (3^9)^1.
Therefore, 3/(3^9) is equivalent to 3/(3^9)^1.
Using the property of exponents that states (a^n)^m = a^(n*m), we can simplify (3^9)^1 as 3^9.
Therefore, 3/(3^9)^1 is equivalent to 3/3^9.
Finally, we can simplify 3/3^9 by dividing both the numerator and denominator by 3, which gives us 1/3^8.
So, 37⋅3^(-9) is equal to 1/3^8.
i checked and the answer is wrong
I apologize for the mistake. Let's go through the steps again.
We have 37⋅3^(-9).
Using the property of exponents that says a^(-n) = 1/(a^n), we can rewrite 3^(-9) as 1/(3^9).
Therefore, 37⋅3^(-9) is equivalent to 37 * 1/(3^9).
Now, let's simplify 37 * 1 to just 37.
So, 37⋅3^(-9) is equivalent to 37/(3^9).
To simplify this expression further, we can rewrite 37 as (3^3 + 19) since 3^3 = 27.
Now, our expression becomes (3^3 + 19) / (3^9).
Expanding the numerator, we get (27 + 19) / (3^9).
Simplifying, we have 46 / (3^9).
Therefore, the equivalent expression to 37⋅3^(-9) with only positive exponents is 46 / (3^9), which cannot be simplified any further.
ITS STILL NOT CORRECT
I apologize for the previous errors. Let's try again.
We need to generate equivalent expressions to 37⋅3^(-9) with only positive exponents.
Using the property of exponents that states a^(-n) = 1/(a^n), we can rewrite 3^(-9) as 1/(3^9).
Therefore, 37⋅3^(-9) is equivalent to 37 * 1/(3^9).
Now, let's simplify 37 * 1 to just 37.
So, 37⋅3^(-9) is equivalent to 37/(3^9).
To simplify this expression further, we can rewrite 37 as (3^3 + 28) since 3^3 = 27.
Now, our expression becomes (3^3 + 28) / (3^9).
Expanding the numerator, we get (27 + 28) / (3^9).
Simplifying, we have 55 / (3^9).
Therefore, the equivalent expression to 37⋅3^(-9) with only positive exponents is 55 / (3^9).
To solve this expression, we can simplify it further by evaluating 3^9.
3^9 equals 19683.
So, our final expression is 55 / 19683. This is the simplified fraction with no remaining exponents.
pply the Properties of Integer Exponents to generate equivalent expressions to 222−4 with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
222−4=