Ty said:
A number to the 10th power is divided by the same number to the 7th power is 125. What is the number? Explain the reasoning to show your work. :?: :?: :?:
This one is easier than you think.
X^10/X^3=125
If you know how to divide the two X numbers and their exponents, you should be able to reduce to a whole number. This leaves you with X^?=125. ? = the mystery exponent.
The next step is to get rid of the X exponent in order to solve for X. Once you know the mystery exponent, you should then be able to fairly easily figure out what the ^? root of 125 is. The squared, cubed, fourth, etc. root of a number is found by changing the power of the number to the reciprocal of its exponent. For example, the square root of X can also be expressed as X^1/2. Cube root would be X^1/3, fourth root X^1/4, etc.
Therefore, in order to find the value of X, you must get rid of its exponent and deal with your actual number in the same way. Remember that you should always do the same process on both sides of an equation.. if you're adding to one side, you add to the other. If you find the root of one side, you have to find the root of the other.
X^? = 125 would then be X = 125^1/?
As an example, X^2 = 125 .. then.. X = 125^1/2
When you reduce to find the final exponent of X that equals 125, plug 125^(1/?) into a calculator (i.e. graphing), making sure you use parentheses around the entire exponent -- X^(1/2) -- and voila.
-- Alena
