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

Question

By simplifying 25 to 5^2 to make both powers base five and subtracting the exponents
	By simplifying 25 to 5^2 to make both powers base five and adding the exponents
	By finding the quotient of the bases to be  and cancelling common factors
	By finding the quotient of the bases to be  and simplifying the expression

Answer 1

???????????????????????? "quoeshent av power" ?????????????????????

never herd av such a dum werd

5^4/25=(25*25)/25=25

nuthun tuit

Answer 2

 haha

Answer 3

5^4/25

= (5^4)/(5^2)

The quotient of powers allows you to subtract exponents when dividing by powers of the same base:

= 5 ^ (4-2)

=5 ^ 2

= 25

I'm not sure I fully understand what the teacher is after in the second and third questions, but you can move a numerator to a denominator by inverting it (1 / x), which is the same as taking it to the power of -1:

1 / ((5 ^ -4) x (5 ^ 2))

= 1 / (5 ^ (-4 + 2))

= 1 / 5 ^ -2

And the same reasoning applies to taking a denominator back to the numerator, viz changing the sign of the exponent:

= 5 ^ 2 = 25