Answer:
x = 14
y = 4
z = 3
Explanation:
let's start with the top of the first fraction. to combine an exponent that has its own exponent, you multiply the exponents together. when it's outside a set of parentheses like that, it applies to everything in the parentheses.
(a⁻³c²)⁻⁴ multiply -4 by both exponents
a¹²c⁻⁸
now we can clean up the bottom of that fraction.
(ab)⁻¹c⁻⁹
to clean it up, we distribute the -1 through the parentheses by multiplying it by the pre-existing exponents (which are 1)
a⁻¹b⁻¹c⁻⁹
now we can simplify that fraction as a whole. remember, when we divide numbers, we subtract their exponents.
a¹²c⁻⁸
a⁻¹b⁻¹c⁻⁹
we can simplify a and c, so we can subtract their exponents from each other
a¹² a ⁻¹ = a¹³
c⁻⁸ c⁻⁹ = c¹ or c
since there is no simplifying b, it remains the same
a¹³c
b⁻¹
because the second fraction is already clean, we can now move on and combine the fractions. remember, when multiplying, we add the exponents.
a¹³c × a
b⁻¹ × b⁻³c⁻²
a¹³ × a¹ = a¹⁴
b⁻¹ × b⁻³ = b⁻⁴
c¹ × c⁻² = c³
we now have:
a¹⁴c³
b⁻⁴
all we do now is move b to the top and switch the negative to a positive
a¹⁴c³b⁴
lmk if i need to explain it differently :)