Answer:
1) 5
2) 5
Step-by-step explanation:
Data provided in the question:
(3²⁷)(5¹⁰)(z) = (5⁸)(9¹⁴)([tex]x^y[/tex])
Now,
on simplifying the above equation
⇒ (3²⁷)(5¹⁰)(z) = (5⁸)((3²)¹⁴)([tex]x^y[/tex])
or
⇒ (3²⁷)(5¹⁰)(z) = (5⁸)(3²⁸)([tex]x^y[/tex])
or
⇒ [tex](\frac{3^{27}}{3^{28}})(\frac{5^{10}}{5^8})z=x^y[/tex]
or
⇒[tex](\frac{5^2}{3})z=x^y[/tex]
or
⇒[tex]\frac{5^2}{3}=\frac{x^y}{z}[/tex]
we can say
x = 5, y = 2 and, z = 3
Now,
(1) y is prime
since, 2 is a prime number,
we can have
x = 5
2) x is prime
since 5 is also a prime number
therefore,
x = 5
