Let x, y, and z be positive numbers. What is the fourth root of the expression:
16x^8 * y^4 * z^16
What is a "fourth root"?
Thank you! :-)
Fourth root is the same as to the 1/4th power, just like square root is the same as to the 1/2th power.
Answer is:
16x^2 * y * z^4
you must of course also take the fourth root of 15 which is 2, so ...
2x^2 * y * z^4
You are right Reiny. I got a little sloppy there and missed that.
The fourth root of a number refers to finding the number that, when raised to the power of 4, gives you the original number. In other words, it is the inverse operation of raising a number to the power of 4.
To calculate the fourth root of the expression 16x^8 * y^4 * z^16, we need to find the number that, when raised to the power of 4, equals the given expression.
The first step is to simplify the expression by using the properties of exponents. We can rewrite the expression as:
16 * x^(8/4) * y^(4/4) * z^(16/4)
Simplifying further:
16 * x^2 * y * z^4
Now, we can calculate the fourth root by taking the fourth root of each term individually:
Fourth root of 16 = 2
Fourth root of x^2 = x^(2/4) = x^(1/2) (since dividing exponents means taking the root)
Fourth root of y = y^(1/4)
Fourth root of z^4 = z^(4/4) = z^1 = z
Combining these results:
Fourth root of 16x^8 * y^4 * z^16 = 2 * x^(1/2) * y^(1/4) * z
Therefore, the fourth root of the expression 16x^8 * y^4 * z^16 is 2 * x^(1/2) * y^(1/4) * z.