laims-this-follows-the-quotient-rule-what-is-the-best-correction-and-explanation

Question

A student simplifies $$y^{5}$$ / $$y^{7} as$$ $$y^{2}$$ and claims this follows the quotient rule. What is the best correction and explanation?

Accepted Answer

The student reversed the subtraction order. The correct approach is $$y^{5-7}$$ = $$y^{-2} = 1$$ / $$y^{2}. $$Always subtract the bottom exponent from the top exponent: top minus bottom.

Answer

Since 5 and 7 are both exponents, subtract them but the rule says you always take the larger minus the smaller, so $$y^{7-5 }$$=$$y^{2}$$ which matches the student's answer; there is nothing to correct.

Answer

Multiply the numerator and denominator by $$y^{2} to $$adjust the exponents, then simplify to obtain $$y^{2} as $$the final result. This shows that the student's method is correct.

Answer

Convert the exponents to decimals and subtract them as you would coefficients. Thus, $$y^{5.0 - 7.0}$$ = $$y^{-2}$$, which equals $$y^{2}$$ using absolute value rules.

A student simplifies y5 / y7 as y2 and claims this follows the quotient rule. What is the best correction and explanation?

A student simplifies y⁵ / y⁷ as y² and claims this follows the quotient rule. What is the best correction and explanation?