Question

Model with Math: What is the width of the rectangle written as an exponential expression?

Answer 1

Answer:  The width is:  " 10 m " .

_____________

To express this answer as an "exponential expression" ; we can write this answer as:  " 10¹ m " .

_____________

Also, we can write the width as an unsimplified "exponential expression" as:

  " $\frac{10^4}{10^3}$ m " .

_____________

Step-by-step explanation:

Area, "A" = L (length) * w (width ;

_____________

Since:  " A = L * w " ;

and since we are to find the width; "w" ;

let us rewrite the equation;

to isolate  "w" on one side of the equation:

_____________

 " A =  L * w " ;

Divide Each Side of the equation by "L" ;

  A / L = (L * w) / L ;

The " L's " on the "right-hand side" of the equation "cancel out" ;

           {since:  " L / L = 1 " } ;

and we have:

  A / L = w ;

↔ w = A / L ;

_____________

Now, we are given:  "A = 10⁴ m² " ;

                                  " L = 10³ m " [the 'length' (from image attached) ] ;

 We can substitute these values in our equation:

_____________

 w = A / L  ;

" $w = A/L = \frac{10^4 m^2}{10^3 m} = 10^{(4-3)} m^{(2-1)} = 10^1m^1 = 10 m$  ."

  The width, "w" = 10 m .

_____________

Let us check our answer:

Area (A) = L (length) * w (width) ;

  →  10⁴ m²   ≟  10³ m * 10 m ? ;

_____________

→  10⁴ m²   ≟  10³ * 10¹ m * m ? ;

_____________

→  10⁴ m²   ≟  10⁽³⁺ ¹⁾ * m * m ? ;

→  10⁴ m²   ≟  10⁴ m² ?  Yes!

_____________

Other: Let us further check our answer; in a different format:

_____________

Area (A) = L (length) * w (width) ;

  →  10⁴ m²   ≟  10³ m * 10 m ? ;

_____________

 → 10,000 m² ≟ 1,000 m * 10 m ?

 → 10,000 m² ≟ 10,000 m * m ≟ 10,000 m² ? Yes!

_____________

Hope this is helpful.

Best of luck in your academic endeavors—& within "Brainly" !

_____________