6.
(01.03 HC)
Tom simplified an expression in three steps, as shown:
x to the power of negative 2 multiplied by y to the power of 4, over y multiplied by x to the power of 4 multiplied by x to the power of 4 multiplied by y to the power of negative 2, the whole to the power of 4 equal to x to the power of 2 multiplied by y to the power of 8, over y to the power of 4 multiplied by x to the power of 8 multiplied by x to the power of 8 multiplied by y to the power of 2 equal to x to the power of 2 multiplied by y to the power of 8, over y to the power of 6 multiplied by x to the power of 16.
Which is the first incorrect step and why? (5 points)
Step 1, all the exponents are increased by 4
Step 2, the exponents of the same base are added during multiplication
Step 3, the exponents of the same base are subtracted during division
Step 3, all the exponents are added during division
I think it's the last one but I'm not sure could someone check if I'm right?
type it again, using math notation, and maybe my eyes will stop bleeding.
y^8, x^2/y^3, etc. Lose all the words cluttering things up.
recall that
x^a * x^b = x^(a+b)
and so on
The problem is: (x^-2y4 / yx^4 *x^4y^-2) ^4 = step 1: ( x^2y^8 / y^4x^8 * x^8y^2) = step 2: (x^2y^8 / y^6x^16) = step 3: x^-14 * y^2
To identify the first incorrect step, let's analyze the given expressions and steps taken by Tom.
Step 1: x^(-2) * y^4 / (y * x^4 * x^4 * y^(-2))^4 = x^2 * y^8 / (y^4 * x^8 * x^8 * y^2)
Step 2: x^2 * y^8 / (y^4 * x^8 * x^8 * y^2) = x^2 * y^8 / (y^6 * x^16)
Step 3: x^2 * y^8 / (y^6 * x^16) = (x^2 * y^8 / y^6) * (1 / x^16) = x^2 * y^8 / (y^6 * x^16)
Given that the equation results in x^2 * y^8 / (y^6 * x^16) in all three steps, we can conclude that Steps 1 and 2 are correct. Therefore, the first incorrect step is Step 3, where all the exponents should have been subtracted during the division. However, in Step 3, all the exponents were added instead, resulting in the same expression as Step 2.
Hence, Step 3, where all the exponents are added during division, is the first incorrect step.