(5.3 x 10^4 ) + (1.3 x 10^4 )

i have to express it into scientific notation and than find the significant figure.

The  " 6.6 * 10 ⁴ " .

Explanation:

(5.3 * 10⁴) + (1.3 * 10⁴) = (5.3 + 1.3) * 10⁴ ;

Note:  "2a + 3a = (2+3) a = 5a " ; 

In other words, we are combining the "like terms" ;

(5.3 + 1.3) * 10⁴  =  6.6 * 10⁴ .  

We retain the "2 (two) significant figures" ; because "5.3" and "1.3" both have 2 (two) significant figures.

The  " 6.6 * 10⁴ "  ;  is already written in scientific notation.

(Note:  To write a number in scientific notation; one takes the nearest "non-zero, whole number" that appears to the nearest "left side of the number", writes down that "digit:.  Then, if there are any numbers to the left or right or that number, one writes a "decimal point" after the aforementioned digit.  
 Then, one writes the "multiplication sign" (i.e, the [*] or [ˣ]  symbol) ; then followed by the number; "10",  raised to the appropriate exponent ("power").
If the aforementioned [single, aforementioned, non-zero, integer digit]  has numbers ["digits"] to to the left, then the exponent {"power"] digit written IS that very [number of digits; i.e, number of decimal spaces] to the left [of that aforementioned, single, non-zero, integer digit] ; yet the actual "exponent" {"power"} digit is:  "-4" ;  since we are counting to the LEFT.

Examples:

  " 0.0000404 " ;  written in "scientific notation" ; is:

   " 4.04 * 10⁻⁴ " .   {Note:  The "10 ⁻ ⁴ "  ;  the  "FOUR"  (in the "-4") comes from moving back "FOUR (4) decimal places".  
 
Other example:
  " -0.0003 ";  written in scientific notation; is:  " 3 * 10⁻⁴ ".
  
If the digits are to the "right" of the "whole number digit" that was written down; then the appropriate number is a positive number".  NOTE:  FOR THE APPROPRIATE "exponent" or "power";  if one is dealing with a decimal value, and the decimal value ends in a "zero" as given; or, as an obtained measurement; then we include the "zero" when converted that value to scientific notation.

Example:

  70 ; written in scientific notation; is:  "7 * 10¹ " .

  70.0 ; written in scientific notation; is: "7.00 * 10¹ "

  - 0.05 ; written in scientfic notation; is:  " -5 * 10⁻² " .

  0.0600 ; written in scientific notation is:  "6.0 * 10⁻² " .

NOTE:  I provide this explanation to show that our answer ;

  6.6 * 10⁴ ;  is already in scientific notation; and that the number of significant figures is correct;  since both values in the original problem have exactly 2 (TWO) significant figures.

It conforms what ever surface its in.