5 Problems - SHOW ALL WORK!
x^8/x^2
x^16/x^12
x^25/x^14
8x^6/2x^4
Why do we subtract exponents when we are dividing like bases?
To solve these problems, we can subtract the exponents because when we divide like bases, we are essentially cancelling out the common factors. The exponent of the numerator represents the number of times the base is multiplied by itself, and the exponent of the denominator represents the number of times the base is divided by itself. Subtracting the exponents reflects the division in terms of the number of times the base is divided.
For example, let's solve the first problem: x^8 / x^2.
x^8 / x^2 = x^(8-2) = x^6
Therefore, x^8 / x^2 simplifies to x^6.
Now let's solve the second problem: x^16 / x^12.
x^16 / x^12 = x^(16-12) = x^4
Therefore, x^16 / x^12 simplifies to x^4.
Next, let's solve the third problem: x^25 / x^14.
x^25 / x^14 = x^(25-14) = x^11
Therefore, x^25 / x^14 simplifies to x^11.
Now, let's solve the fourth problem: 8x^6 / 2x^4.
8x^6 / 2x^4 = 8/2 * (x^6 / x^4) = 4x^(6-4) = 4x^2
Therefore, 8x^6 / 2x^4 simplifies to 4x^2.
Overall, we subtract exponents when dividing like bases to cancel out the common factors and simplify the expression.