Question

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?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.Step 1, all the exponents are increased by 4Step 2, the exponents of the same base are added during multiplicationStep 3, the exponents of the same base are subtracted during divisionStep 3, all the exponents are added during division

Answer 1

Remember the following rules of exponents:

$\begin{gathered} (ab)^n=a^nb^n \\ (\frac{a}{b})^n=\frac{a^n}{b^n} \\ (a^n)^m=a^{n\times m} \\ a^n\cdot a^m=a^{n+m} \end{gathered}$

According to the third rule, all the exponents should have been multiplied by 4 rather than increasing them by 4 in the first step.

Therefore, the first incorrect step is Step 1, since all the exponents are increased by 4.