64 negative cubed divided by 4 to the negative fifth.
the answer is 1/256.
Everytim I do this problem i keep getting 256. Can anyone help me?? PLEASE :)
(64^-3)
--------
4^-5
is the same as
4^5
-----
64^3
but 64 = 8*8 = 4*4*4 = 4^3
so we really have
4^5
----
(4^3)^3
which is
4^5
------
4^9
which is
1/4^4
wich is
1/16^2
which is
1/256 yes, they won
Thank you :)
Of course! I can help you understand how to get the correct answer. Let's break down the problem step by step, and I'll explain the process along the way.
The expression you provided is:
64^(-3) / 4^(-5)
To simplify this expression, we'll start by working with the numerators and denominators separately.
Let's focus on the numerator, which is 64^(-3).
To find the value of 64^(-3), recall that a negative exponent indicates the reciprocal of the base raised to the positive exponent. So, to make the exponent positive, we need to take the reciprocal of the base raised to the positive equivalent of the exponent.
In this case, we need to find the reciprocal of 64^3, which means we need to find the cube root of 64.
The cube root of 64 is 4 because 4 * 4 * 4 = 64.
So, 64^(-3) is equal to (1/64^3), which simplifies to 1/262,144.
Now, let's move on to the denominator, which is 4^(-5).
Similar to the previous step, we need to find the reciprocal of 4^5, which means we need to find the fifth root of 4.
The fifth root of 4 is also 4 because 4^5 = 1024.
So, 4^(-5) is equal to (1/4^5), which simplifies to 1/1024.
Now that we have simplified the numerator and denominator separately, we can combine them back into the original expression:
(1/262,144) / (1/1024)
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.
So, (1/262,144) * (1024/1) equals 1024/262,144.
Now, let's simplify this fraction. Both the numerator and denominator have a common factor of 1024. We can divide both by 1024, resulting in:
1/256
Therefore, the answer to the expression 64^(-3) / 4^(-5) is 1/256.
I hope this explanation helps you understand how to solve the problem.