Hey, im a little confused with this question:
2^n x 4^(n+1)
/
8^(n-2)
I have to change all bases to 2 then simplify fully.
Thanks everoyne.
Here are some hints:
4^(n+1) = (2^2)^(n+1)
8^(n-2) = (2^3)^(n-2)
yep ive got that much correct then, im more or less checking if what ive done is correct, that's all.
The final answer i got was
2^(3n+2)
/
2^(3n-6)
Or can that be simplified further?
To simplify the given expression and change all bases to 2, we can use the properties of exponents and rewrite each term.
We start by changing the base of 4 to 2. We can express 4 as 2^2 since 2^2 equals 4. Therefore, we have:
2^n x (2^2)^(n+1)
/
8^(n-2)
Next, we simplify and expand the exponents:
2^n x 2^(2(n+1))
/
(2^3)^(n-2)
Now, we can apply the properties of exponents further. We know that (a^m)^n equals a^(m*n), so we can rewrite the expression as follows:
2^n x 2^(2n + 2)
/
2^(3(n-2))
Now, we can simplify both the numerator and denominator.
In the numerator, we can combine the exponents of 2:
2^(n + 2n + 2)
/
2^(3n - 6)
Simplifying further, we have:
2^(3n + 2)
/
2^(3n - 6)
To divide two expressions with the same base, we subtract the exponents:
2^(3n + 2 - (3n - 6))
Simplifying the subtraction:
2^(3n + 2 - 3n + 6)
We continue the simplification:
2^(6 + 2)
Finally, we add the exponents:
2^8
Therefore, the simplified expression with all bases changed to 2 is 2^8.