my msth finals are tomorrow! please help ASAP. it is applying properties of rational expontents by multipyling. Here goes: (16x^2y)^1/3 times (4x^5y^2z)^1/3 PLEASE HELP! ITS DUE TOMORROW! THANK YOU!
=(16*x^2*y*4*x^5*y^2*z)^1/3=
=(64*x^7*y^6*z)^1/3=
=64^1/3*(x^7)^1/3*(y^6)^1/3*z^1/3=
4*x^(7/3)*y^2*z^1/3
To simplify the expression (16x^2y)^(1/3) times (4x^5y^2z)^(1/3), you can apply the property of rational exponents which states that (a^m)^n = a^(m*n).
Let's break down the expression step by step:
Step 1: Apply the property of rational exponents to each term separately.
(16x^2y)^(1/3) = 16^(1/3) * (x^2)^(1/3) * y^(1/3)
(4x^5y^2z)^(1/3) = 4^(1/3) * (x^5)^(1/3) * (y^2)^(1/3) * z^(1/3)
Step 2: Simplify the individual terms inside each parentheses.
16^(1/3) = 2
(x^2)^(1/3) = x^(2/3)
y^(1/3) remains the same
4^(1/3) = 4^(1/3) = 4^(1/3) = 1.5874 (approx.)
(x^5)^(1/3) = x^(5/3)
(y^2)^(1/3) = y^(2/3)
z^(1/3) remains the same
Step 3: Combine the simplified terms by multiplying them together:
2 * 1.5874 * x^(2/3) * x^(5/3) * y^(1/3) * y^(2/3) * z^(1/3)
Step 4: Multiply the coefficients (numbers) together:
2 * 1.5874 = 3.1748 (approx.)
Step 5: Simplify the variables by adding the exponents:
x^(2/3) * x^(5/3) = x^(2/3 + 5/3) = x^(7/3)
y^(1/3) * y^(2/3) = y^(1/3 + 2/3) = y^(3/3) = y^1 = y
z^(1/3) remains the same
Overall, the simplified expression is:
3.1748 * x^(7/3) * y * z^(1/3)
This is the simplified form of the given expression.