Question

Find the value of x that makes this statement true

Answer 1

$\frac{(-2)^{5x-3}}{(-2)^{2x}} =(-2)^{21}$

$(-2)^{5x-3-2x}=(-2)^{21}$  (The numerator and the denominator has same bases, therefore the powers will get subtracted. It is an exponential property)

$(-2)^{3x-3}=(-2)^{21}$

$3x-3=21$  (As the left hand side is equal to right hand side and the bases are on both the sides are equal too, we will equate their exponential power. Another property)

$x-1=7$

$x=8$  (After simplifying more, you'll get this)