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DᴀʀᴋPᴀʀᴀᴅᴏx

[tex]\huge \bf༆ Answer ༄[/tex]

Let's solve ~

  • [tex] \sf(ab) {}^{37} \times (ab) {}^{42} \times (ab) {}^{51} [/tex]

If the numbers with same same base are multiplied them, their exponents add up ~

  • [tex] \sf(ab) {}^{37 + 42 + 51} [/tex]

  • [tex] \sf(ab) {}^{130} [/tex]

And we can also separate the base (when multiplied) to different bases with having same exponent as the original one.

  • [tex] \sf{a {}^ {130} }{ \times b {}^{130} }[/tex]

HayabusaBrainly

======== [tex]\huge{\bf{Answer :}}[/tex] ========

[tex] \bold{ \underline{Given : -}}[/tex]

  • (ab)³⁷ • (ab)⁴² • (ab)⁵¹

[tex] \: [/tex]

[tex] \bold{ \underline{To \: Find : - }}[/tex]

  • Find to result!

[tex] \: [/tex]

[tex] \bold{ \underline{Solution : - }}[/tex]

Did you know that there are exponential properties of matter such as the following :

  • [tex] \sf {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

Soo :

[tex] \sf \longmapsto (ab {)}^{37} \times {(ab)}^{42} \times {(ab)}^{51} [/tex]

[tex] \sf \longmapsto {(ab)}^{37 + 42} \times {(ab)}^{51} [/tex]

[tex] \sf\longmapsto (ab {)}^{79} \times {(ab)}^{51} [/tex]

[tex] \sf \longmapsto {(ab)}^{79 + 51} [/tex]

[tex] \sf \longmapsto \boxed { \bold{ \red{ {(ab)}^{130}}}} [/tex]

[tex] \: [/tex]

[tex] \bold{ \underline{ \: Conclusion : -}}[/tex]

  • [tex] \sf( {ab)}^{37} \times {(ab)}^{42} \times {(ab)}^{51} = \bf {(ab)}^{130} [/tex]

[tex] \: [/tex]

I hope this helps!

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