Respuesta :

Answer:

[tex]\boxed{\boxed{\sf~a:14x^5y^7z^{15}}}[/tex]

Solution Steps:

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

  • Area [tex]=\sf{H}[/tex] × [tex]\sf{W}[/tex]
  • Area [tex]=7x^4y^2z[/tex] × [tex]2xy^5z^{14}[/tex]

Note:

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

Equation at the end of Step 1:

  • [tex]7x^4y^2z[/tex] × [tex]2xy^5z^{14}[/tex]
  • [tex]2xy^5z^{14}[/tex] × [tex]7x^4y^2z[/tex]

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

  • [tex]x^4+x=x^5[/tex]

Note:

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

 - When you have a plain variable like [tex]x[/tex], you can assume [tex]x=1[/tex].

Equation at the end of Step 2:

  • [tex]7x^5y^2z[/tex] × [tex]2y^5z^{14}[/tex]

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

  • [tex]y^2+y^5=y^7[/tex]

Note:

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

Equation at the end of Step 3:

  • [tex]7x^5y^7z[/tex] × [tex]2z^{14}[/tex]

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

  • [tex]z+z^{14}=z^{15}[/tex]

Note:

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

 - When you have a plain variable like [tex]z[/tex], you can assume [tex]z=1[/tex].

Equation at the end of Step 4:

  • [tex]7x^5y^7z^{15}[/tex] × [tex]2[/tex]

5.) Multiply 7 and 2:

  • [tex]7[/tex] × [tex]2=14[/tex]

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:

  • [tex]14x^5y^7z^{15}[/tex]

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