How do you use the laws of exponents to simplify the expression # ((4^2)/(4^3))*(4)^-3#?

2 Answers
May 21, 2018

Answer:

#1/256#

Explanation:

#"using the "color(blue)"laws of exponents"#

#•color(white)(x)a^m/a^nhArra^((m-n))#

#•color(white)(x)a^mxxa^nhArra^((m+n))#

#•color(white)(x)a^-mhArr1/a^m#

#rArr(4^2/4^3)xx4^-3#

#=4^((2-3))xx4^-3#

#=4^-1xx4^-3#

#=4^((-1+(-3)))=4^-4=1/4^4=1/256#

May 21, 2018

Answer:

#1/4^4 or 4^-4#

Explanation:

When dividing like terms with powers you subtract the powers.

#4^2/4^3=4^(2-3)=4^(-1)#

When multiplying like terms with powers you add the powers

#(4^2/4^3)xx 4^-3=4^(-1)xx4^-3=4^(-1+ -3)4^(-1-3)=4^-4#