Answer:
Proved: xyz = 1
Explanation:
- By the laws of exponents, when a single base has two exponents, the exponents are multiplied. This is known as power of a power property.
[tex](a^{m} )^{n} =a^{mn}[/tex]
Step 1:
We have been given,
[tex]a=c^{z}[/tex] →(1)
[tex]b=a^{x}[/tex] →(2)
[tex]c=b^{y}[/tex] →(3)
Step 2:
Substituting (1) in (2), we get:
[tex]b=(c^{z})^{x}[/tex]
[tex]b=c^{xz}[/tex] →(4)
Substituting (4) in (3), we get:
[tex]c=(c^{xz})^{y}[/tex]
[tex]c=c^{xyz}[/tex]
Step 3:
We know that c = c¹
[tex]c^1=c^{xyz}[/tex]
Since the base numbers on both sides are the same, equating the exponents on both sides,
[tex]xyz = 1[/tex]
Conclusion:
Hence, it is proved that xyz = 1
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