(5)^-1/2 * (5x)^5/2 (5x)^-3/2 =
1/5*sqrt5x^5(1/sqrt5x^3)=
sqrt5x^5/sqrt5*sqrt5x^3=
x^2 sqrt5x/ sqrt5 * x sqrt5x=
x^2/x sqrt5=
x/sqrt 5
Is this correct? If not, where am I going wrong and what is the answer?
The way it is actually written is
(5)^-1/2 * 5x^5/2 (5x)^-3/2 =
well, 5x^5/2 (5x)^-3/2 = 5x
so, now what do you think?
5x/sqrt5?
I think I understand now. This would be the solution:
(5)^-1/2 * 5x^5/2+(-3/2)=
(5)^-1/2 * 5x=
5x/sqrt5
or, just √5 x, since 5/√5 = √5
Let's go through the steps to verify the simplification of the expression:
(5)^(-1/2) * (5x)^(5/2) * (5x)^(-3/2)
Step 1: Simplify the exponent of the first term using the power rule for exponents: a^(-n) = 1 / a^n.
(5)^(-1/2) = 1 / (5)^(1/2) = 1 / sqrt(5)
Step 2: Simplify the exponent of the second term using the power rule for exponents: (ab)^n = a^n * b^n.
(5x)^(5/2) = (5)^(5/2) * (x)^(5/2) = sqrt(5^5) * sqrt(x^5) = sqrt(5^5 * x^5) = sqrt(5^5x^5)
Step 3: Simplify the exponent of the third term using the power rule for exponents: a^(-n) = 1 / a^n.
(5x)^(-3/2) = 1 / (5x)^(3/2) = 1 / (sqrt(5x)^3) = 1 / (sqrt(5^3 * x^3)) = 1 / (sqrt(5^3) * sqrt(x^3)) = 1 / (sqrt(5^3 * x^3)) = 1 / sqrt(5^3x^3)
Now, let's substitute these simplified terms back into the original expression:
1 / sqrt(5) * sqrt(5^5x^5) * 1 / sqrt(5^3x^3)
Taking the products under one square root:
1 * sqrt(5^5x^5) * 1 / (sqrt(5) * sqrt(5^3x^3))
This simplifies to:
sqrt(5^5x^5) / (sqrt(5) * sqrt(5^3x^3))
Taking out the square roots separately:
(sqrt(5^5) * sqrt(x^5)) / (sqrt(5) * (sqrt(5^3) * sqrt(x^3)))
Simplifying:
(sqrt(5^5) * x^2) / (sqrt(5) * (5 * sqrt(x^3)))
Simplifying further:
(sqrt(5^5) * x^2) / (5 * sqrt(5) * sqrt(x^3))
Simplifying the square root term:
(sqrt(5^5) * x^2) / (5 * sqrt(5) * x(sqrt(x)))
We can cancel out the x term:
(sqrt(5^5) * x^2) / (5 * sqrt(5) * sqrt(x))
Finally, simplifying the square root term:
(sqrt(5^5) * x^2) / (5 * sqrt(5) * sqrt(x)) = (x^2 * sqrt(5^5)) / (5 * sqrt(5) * sqrt(x))
So, the correct simplification is:
(x^2 * sqrt(5^5)) / (5 * sqrt(5) * sqrt(x))
And it cannot be simplified further. Therefore, the answer you provided, x / sqrt(5), is not correct.