Question

Simplify that a^x-y . a^y-z . a^z-x​

Answer 1

Answer:

a^x-y.a^y-z.a^z-x

a^x-y+y-z+z-x

a^0

1

Answer 2

The simplified form of the expression is 1.

Step-by-step explanation:

The given expression is

$a^{x-y}\cdot a^{y-z}\cdot a^{z-x}$

Apply the product rule of exponents : $a^x\cdot a^y = a^{x+y}$

$a^{x-y+y-z}\cdot a^{z-x}\\\\=a^{x-z}\cdot a^{z-x}$

Again apply  the product rule of exponents

$a^{x-z+z-x}\\\\=a^0$

Any number (excluded zero) with exponent zero is 1.

$a^0\\\\=1$

Therefore, the simplified form of the expression is 1.

#Learn More:

If 3^x-1=9 and 4^y+2=64, what is the value of x/9?

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