Question

27 exponent x divided by 3 is equal to one divided by 81.​

Answer 1

Answer:

x = -1

Step-by-step explanation:

27 exponent x =  $27^x$

Divided by 3 =   $\frac{27^x}{3}$

Is equal to : $\frac{1}{81}$

Therefore,

         $\frac{27^x}{3} = \frac{1}{81}$

Cross multiplying :

       $27^x \times 81 = 1 \times 3$

       $27^x = \frac{3}{81}$

       $27^x = \frac{1}{27}$

       $27^x = 27^{-1}$

         $x = -1$                     $[a^x = a^y => x = y]$

Answer 2

27 exponent x/3 = 1/81

we can say exponent as power also

(27 power x) × (3 power -1) = 81 power -1

(3 power 3x) × ( 3 power -1) = 3 power -4

IN MULTIPLICATION WHEN BASES ARE SAME THEN POWERS ARE ADDED

3 power 3x + (-1) = 3 power -4

IN AN EQUATION WHEN BASES ARE EQUAL POWERS ALSO EQUAL

3x +(-1) = -4

3x - 1 = -4

3x = -4 + 1

3x = -3

x = -3/3

x = -1