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Which expression represents

the area of a rectangle with
sides measuring 7x4y2z units and
2xy5z14?

Which expression represents the area of a rectangle with sides measuring 7x4y2z units-example-1
User Ken Ma
by
8.4k points

1 Answer

2 votes

Answer:


\boxed{\boxed{\sf~a:14x^5y^7z^(15)}}

Solution Steps:

______________________________

1.) To solve this you must first know the formula for area of a rectangle:

  • Area
    =\sf{H} ×
    \sf{W}
  • Area
    =7x^4y^2z ×
    2xy^5z^(14)

Note:

- It doesn't matter which measurement fills the height or width part in the formula.

Equation at the end of Step 1:


  • 7x^4y^2z ×
    2xy^5z^(14)

  • 2xy^5z^(14) ×
    7x^4y^2z

2.) Add 4 and 1, (x powers:)


  • x^4+x=x^5

Note:

- To multiply powers of the same base, you can add their exponents. So you just do
4+1=5.

- When you have a plain variable like
x, you can assume
x=1.

Equation at the end of Step 2:


  • 7x^5y^2z ×
    2y^5z^(14)

3.) Add 2 and 5, (y powers:)


  • y^2+y^5=y^7

Note:

- To multiply powers of the same base, you can add their exponents. So you just do
2+5=7.

Equation at the end of Step 3:


  • 7x^5y^7z ×
    2z^(14)

4.) Add 1 and 14, (z powers:)


  • z+z^(14)=z^(15)

Note:

- To multiply powers of the same base, you can add their exponents. So you just do
1+14=15.

- When you have a plain variable like
z, you can assume
z=1.

Equation at the end of Step 4:


  • 7x^5y^7z^(15) ×
    2

5.) Multiply 7 and 2:


  • 7 ×
    2=14

Note:

- Since we combine all the powers and multiplied the bases, all you have to do is put it all together in 1 form like we were doing after we added powers in the earlier steps.

Equation at the end of All Steps:


  • 14x^5y^7z^(15)

______________________________

Which expression represents the area of a rectangle with sides measuring 7x4y2z units-example-1
User James Mertz
by
7.7k points

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