P=(64)^-2
Q=1/16^(1/3)
R=8root2
Express pqr as a power of 4
P=4^(-6)
Q=4^(-2/3)
R= ????????
How can i find R?
*please show me the method for future reference*
Thankyou
Using the numbers 3,2 and , which of these problems would have a solution of 4
whats the answer
4 x 2^3/2^3
2 x 2^3/2^4
3 x 2^3/2^4
3 x 2^4/2^4
Erm the first one?
Acutally the second one as 4^3/2^4
no it was actually the first one i turned it in but it said it was the first one but its ok i still got a B
The first one
4x2^3/2^3 =4
Why am i using numbers 3and2. R is 8root2
What is all this nonsense?
Notice all 3 powers can be expressed as a power with base 2, thus as a power with base 4
P = (64)^-2
= (4^3)^-2 = 4^-6
Q = (1/16)^(1/3)
= 16^(-1/3)
= (4^2)^-1/3) = 4^(-2/3)
R = 8√2
= 2^3(2^(1/2))
= 2^(7/2)
= (4^(1/2))^(7/2)
= 4^(7/4)
the PQR = (4^-6)(4^(-2/3))(4^(7/4))
= 4^(-6-2/3+7/4)
= 4^(-59/12)
To find the value of R and express it as a power of 4, we will first determine the value of R.
Given that R = 8√2, we can rewrite this as R = 8 * (2^(1/2)).
Now, we can simplify the expression further.
R = 8 * (sqrt(2))
To express R as a power of 4, we need to rewrite the expression in terms of 4.
Since 2 can be expressed as 2^2, and the square root of a number is equivalent to raising the number to the power of 1/2, we can rewrite R as:
R = 8 * (2^(1/2))
= 8 * ((2^2)^(1/2))
= 8 * (2^(2 * 1/2))
= 8 * (2^1)
= 8 * 2
= 16
Therefore, R = 16, which can be expressed as 16 = 4^2.
So, the final expression of PQR as a power of 4 is:
PQR = (4^(-6)) * (4^(-2/3)) * (4^2)
= 4^(-6 - 2/3 + 2)
= 4^(-20/3)
Thus, PQR can be expressed as 4^(-20/3).