Question

find the value of x​

Answer 1

Answer:

X= -1 is the answer for this question

Answer 2

Answer:

$x = -1$

Step-by-step explanation:

    $\frac{a^{-3} *b^{-4}}{a^{-2}*b^{-3}} = (ab)^{x}$

We can write this as:

    $\frac{a^{-3} }{a^{-2}} * \frac{b^{-4}}{b^{-3}} = (ab)^{x}$

We know that $\frac{a^{m}}{a^{n}} = a^{m-n}$

⇒ $(a^{[-3-(-2)]})(b^{[-4-(-3)]})= (ab)^{x}$

⇒ $(a^{(-3+2)})(b^{(-4+3)})= (ab)^{x}$

⇒ $(a^{-1})(b^{-1}) = (ab)^{x}$

We know that $a^{m}*b^{m}= (ab)^{m}$

⇒ $(ab)^{-1}= (ab)^{x}$

Since, the base of the exponentials are the same we can remove them

⇒ $-1 = x$