Explain how the Quotient of Powers was used to simplify this expression.

5^4/25 = 5^2 @mathmale

Question

Explain how the Quotient of Powers was used to simplify this expression.

 5^4/25 = 5^2 @mathmale

anonymous · Answer

Would you like the question's options?

mathmale · Answer

I did hope you'd use my suggestion (to use parentheses for additional clarity).  Please re-write your expression so I know whether you mean   (5^4) / 25    or 5^(4/25).

anonymous · Answer

Sorry it's (5^4)/25 = (5^2)

anonymous · Answer

I think you're supposed to make 25 into an exponent and then subtract the exponents to get (5^2)

mathmale · Answer

Huge difference in clarity.  Thank you.   $$\frac{ 5^4 }{ 25 }=?$$  Do you see any way of reducing this by manipulating the base and exponent?

mathmale · Answer

Leave that 5^4 as is.  Rewrite 25 as a power of 5.  Then follow your own suggestion regarding the exponents.

anonymous · Answer

So you're supposed to subtract the exponents in the end?

mathmale · Answer

Exactly!

anonymous · Answer

Oh ok thank you so much !

mathmale · Answer

$$\frac{ x^a}{ x^b }=x ^{a-b}$$

mathmale · Answer

I ask for a bit more effort up front, so that you eliminate ambiguity, but trust me, it's worth being crystal clear when you're communicating math.  Happy to work with you.

anonymous · Answer

Same thanks again