If
P=(64)^-2
Q=1/(16)^1/3
R=8root2
Express pqr as
i) a power of 2
ii) a power of 4
p = 2^-12 = 4^-6
q = 2^-(4/3) = 4^(-2/3)
r = 8*2^(1/2) = 2^(7/2) = 4^(7/4)
Now just add up the powers for the product.
The power of 2 and power of 4 are separate questions. So why are we adding the powers?
Come on, guy.
Add the powers of 2 for one answer; add the powers of 4 for the other.
I was just showing how each number could be expressed either as a power of 2 or a power of 4.
Sheesh.
To express PQR as a power of 2 and a power of 4, we need to simplify each of the given values.
Let's start with P:
P = (64)^-2
To simplify this expression, we can rewrite 64 as 2^6:
P = (2^6)^-2
Applying the exponent rule (a^m)^n = a^(m*n), we can multiply the exponents:
P = 2^(6 * -2)
Simplifying further:
P = 2^(-12)
Now let's move on to Q:
Q = 1/(16)^(1/3)
We can rewrite 16 as 2^4:
Q = 1/(2^4)^(1/3)
Again applying the exponent rule:
Q = 1/2^(4 * 1/3)
Simplifying the exponent:
Q = 1/2^(4/3)
Finally, let's consider R:
R = 8√2
To express R as a power, we can rewrite 8 as 2^3 and simplify the square root:
R = 2^3√2
Since the square root can be written as a fractional exponent:
R = 2^3 * 2^(1/2)
Combining the exponents:
R = 2^(3 + 1/2)
R = 2^(7/2)
Now that we have expressed P, Q, and R as powers of 2, we can multiply them.
For PQR as a power of 2:
PQR = 2^(-12) * 1/2^(4/3) * 2^(7/2)
To multiply powers with the same base, we add the exponents:
PQR = 2^(-12 - 4/3 + 7/2)
Now, to express PQR as a power of 4:
PQR = 2^(-12 - 4/3 + 7/2)
To express the power of 2 as a power of 4, we can rewrite 2 as 4^1/2:
PQR = (4^1/2)^(-12 - 4/3 + 7/2)
Again applying the exponent rule:
PQR = 4^((1/2) * (-12 - 4/3 + 7/2))
Simplifying the exponent:
PQR = 4^(-6 - 4/3 + 7/4)
PQR = 4^(-19/12)
Now, PQR has been expressed as a power of 2 and a power of 4.