The power of a quotient rule - simplify
(3y^8/2zy^2)^4
I need help in solving this problem - I do know to solve what is in the parentheses first. by the 4th power...but I need detailed guidance in order to grasp the concept - ty:)
the 4th power on the outside applies to each factor of the inside
(3y^8/2zy^2)^4
= 3^4 y^32/(2^4 z^4 y^8)
= 81y^24 / (16z^4)
or you could have reduced the y's first
(3y^8/2zy^2)^4
= (3y^6/(2z))^4
= 81y^24/(16z^4)
Got it - ty:0)
My next one I think I have figured out - however do we simplify the 10^10?
9x10^-4/3x10^-6 = 3x10^10
Sorry - this is regarding computations w/scientific notation
To simplify the expression (3y^8/2zy^2)^4, follow these steps:
Step 1: Solve what is inside the parentheses first, which involves applying the quotient rule.
Quotient rule: To divide two exponential terms with the same base, subtract the exponents.
So, simplify 3y^8/2zy^2 as follows:
3y^8/2zy^2 = (3/2) * (y^8 / zy^2)
Step 2: Simplify further by dividing 3 by 2, which gives (3/2):
(3/2) * (y^8 / zy^2) = (3/2) * (y^(8-2) / z)
Simplifying the exponent in the numerator:
(3/2) * (y^6 / z)
Step 3: Now we raise the simplified expression to the power of 4.
To raise a term with an exponent to a power, multiply the exponents:
((3/2) * (y^6 / z))^4 = (3/2)^4 * (y^6 / z)^4
Step 4: Simplify each part separately.
(a) Simplify (3/2)^4:
(3/2)^4 = (3^4 / 2^4) = 81/16
(b) Simplify (y^6 / z)^4:
To raise a fraction to a power, raise the numerator and denominator separately.
(y^6 / z)^4 = (y^6)^4 / (z)^4 = y^(6*4) / z^4 = y^24 / z^4
Step 5: Combine the simplified parts.
(3/2)^4 * (y^6 / z)^4 = (81/16) * (y^24 / z^4)
Therefore, the simplified expression is (81/16) * (y^24 / z^4).