Question

what is the value of 4 to the power of 3 multiplied by 4 to the power of -1 multiplied by 5 to the power of -2 divided by 4 to the power of 4 multiplied by 5 to the power of -3 multiplied to the power of 0

Answer 1

Explanation:

the answer is 20

Answer 2

remember
try and group like bases
and
(x^m)(x^n)=x^(m+n)
also
x^0=1
and
(ab)/(cd)=(a/c)(b/d)
and
(x^m)/(x^n)=x^(m-n)
and
x^-m=1/(x^m)


`((4^(3))(4^(-1))(5^(-2)))/((4^(4))(5^(-3))((-3)^(0)))`


simplify a few stuff

on top
(4^3)(4^-1)=4^(3-1)=4^2

on bottom
(-3)^0=1
which cancels out since 1 times x=x so disregard the (-3)^0

now we have

`((4^(2))(5^(-2)))/((4^(4))(5^(-3)))`
split into 2 fractions with 4's in one and 5's in other
(
`(4^(2))/(4^(4))`)(
`(5^(-2))/(5^(-3))`)
remember the exponential law

first fraction

`(4^(2))/(4^(4))`=4^(2-4)=4^-2
second
(
`(5^(-2))/(5^(-3))`)=5^(-2-(-3))=5^(-2+3)=5^1=5

now we have
(4^-2)(5)=(1/(4^2))(5)=5/(4^2)=5/16