Exponential/logarithmic Functions

Question 1

Product Law: (y^m)(y^n)=

Answer 1

y^m+n

ex: (x^2)(x^3)=x^5

Question 2

Power of an exponent: (y^m)^n=

Answer 2

y^mxn

ex: (x^2)^3= (x^2)(x^2)(x^2)=x^6

Question 3

Power of Quotient: (x/y)^m=

Answer 3

Exponent distributes across numerator and denominator
(x^m/y^m)
ex: (10/5)^2=(10^2/5^2)=(100/25)=4
0r: (10/5)^2=(2)^2=4

Question 4

Integral Exponent Rule (Change of sign): 1/x^m=

Answer 4

x^-m
numerator and denominator switch
ex: 1/x^3= x^-3
or: 1/y^-2=y^2

Question 5

Rational Exponent: X^m/n=

Answer 5

(x^1/n)^m

Question 6

Quotient Law: x^m/x^n=

Answer 6

(x^m)(1+x^n-m)=(x^m)+x^m(x^m-n)=x^m+x^n