help me solve this exponential problem
P to the 3rd power times q 5 over 2 all over q to the 2nd power times r to the negative 6.
Oh boy, I'm glad you asked me this question and not a serious mathematician! Let's dive into this exponential circus.
To solve this problem, we'll break it down step by step. Let's start with the numerator: P to the 3rd power times q to the 5 over 2.
Well, if P is going to the 3rd power, it must be practicing its yoga because it's stretching itself out! And q to the 5 over 2? That's just q getting a little tired from running around, taking a break, and catching its breath. So, we have P cubed and q to the power of 5 over 2.
Now, let's move to the denominator: q to the 2nd power times r to the negative 6.
Ah, poor r with a negative exponent, feeling a bit low. But don't worry r, we'll fix that right up.
Now, let's put it all together! We have (P^3 * q^(5/2)) / (q^2 * r^-6).
Since we're dividing, we can subtract the exponents of like terms, just like at the clown circus!
Let's simplify and combine: P^(3 - 2) * q^((5/2) - 2) * r^6.
We can simplify it further: P^1 * q^(1/2) * r^6.
And that's your simplified answer. Even though the problem seemed like a clown act, we've solved it!
Don't take math too seriously, have fun with it!
To solve the problem, we can apply the rules of exponents. Let's break it down step-by-step:
Step 1: Simplify the numerator.
The numerator consists of P to the 3rd power multiplied by q to the power 5/2. To simplify this, multiply the exponents:
P^3 * q^(5/2) = P^3 * √(q^5)
Step 2: Simplify the denominator.
The denominator consists of q squared multiplied by r to the power -6. To simplify this, we use the rule that a negative exponent can be written as the reciprocal of the positive exponent:
q^2 * r^-6 = q^2 * (1/r^6)
Step 3: Write the expression as a single fraction.
Putting both the numerator and denominator together, we get:
(P^3 * √(q^5)) / (q^2 * (1/r^6))
Step 4: Simplify further if possible.
To simplify, we can bring the variable q in the numerator inside the square root:
(P^3 * q^(5/2)) / (q^2 * (1/r^6)) = P^3 * (q^(5/2-2)) * r^6
Simplifying the exponent of q: q^(5/2-2) = q^(5/2-4/2) = q^(1/2)
So, the final simplified expression is:
P^3 * q^(1/2) * r^6
To solve this exponential problem, let's break it down step by step.
The expression you provided is:
(P^3 * q^(5/2)) / (q^2 * r^-6)
1. Simplify the numerator first:
P^3 * q^(5/2)
When multiplying exponential terms with the same base (P^3 and q^(5/2)), you add the exponents. So, the simplified numerator is:
P^3 * q^(5/2) = P^3 * q^(2 + 1/2) = P^3 * q^(2) * q^(1/2) = P^3 * (q^2) * (sqrt(q))
2. Simplify the denominator:
q^2 * r^-6
When dividing exponential terms with the same base (q^2 and r^-6), you subtract the exponents. So, the simplified denominator is:
q^2 * r^-6 = q^2 / r^6
3. Substitute the simplified numerator and denominator back into the original expression:
(P^3 * q^2 * sqrt(q)) / (q^2 / r^6)
4. Now, to divide by a fraction, you can multiply by its reciprocal. So, invert the denominator and multiply:
(P^3 * q^2 * sqrt(q)) * (r^6 / q^2)
5. Simplify the expression further:
P^3 * r^6 * (sqrt(q) / q^2)
And, that's the final simplified form of the expression!