hey i need some help with a couple of questions please.....
change all bases to 2 then simplify fully
2^n x 4^n+1
8^n-2
(note that i cannot put the division line thingo in)
prove that:
a^m/n = n(outside radical sign)a^m (inside radical sign)
i don't know if you can understand that??? if not i will post a link 2 a word doc...
thanx 4 ur help!! :):)
I have a feeling you meant to type
2^n x 4^(n+1) or else the +1 would be a nuisance dangling term
change the last factor
4^(n+1) into [2^2]^(n+1) = 2^(2n+2)
so now you have
(2^n)(2^(2n+2))
= 2^(3n+2)
thanx,
actually the site cut off my question, what i tried to type was
2^n x 4^(n+1)
/
8^(n-2)
then I am sure you can finish the question if your realize that
8^(n-2)
= [2^3]^(n-2)
= 2^(3n-6)
thanks for the help, i appreciate it, i was unsure of where iwas going wrong, it was just my brackets i mucked up, thanx.
Sure, I can help you with those questions. Let's start with the first one.
To change the bases to 2 and simplify, we will use the property of exponents that states a^(b+c) = a^b * a^c.
Let's take the first expression:
2^n x 4^(n+1)
To change the base 4 to base 2, we know that 4 can be expressed as 2^2. So we can rewrite the expression as:
2^n x (2^2)^(n+1)
Using the exponent property, we can simplify further:
2^n x 2^(2n+2)
Since the bases are the same, we can combine the exponents:
2^(n + 2n + 2)
2^(3n + 2)
Now, let's move on to the second expression:
8^n-2
To change the base 8 to base 2, we know that 8 can be expressed as 2^3. So we can rewrite the expression as:
(2^3)^(n-2)
Using the exponent property, we can simplify further:
2^(3(n-2))
Now, let's move on to prove the second statement.
To prove that a^(m/n) = n√(a^m), we will use the property of radicals that states (√x)^n = x^(1/n).
Starting with the left side of the equation: a^(m/n)
We can express the exponent m/n as m * (1/n):
a^(m * (1/n))
Using the exponent property, we can rewrite it as:
(a^m)^(1/n)
Now, we can apply the property of radicals to convert it into a radical form:
n√(a^m)
Therefore, we have proved that a^(m/n) = n√(a^m).
I hope this helps! Let me know if you have any further questions.