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xxTIMURxx [149]
2 years ago
7

Plz simplify with steps

Mathematics
2 answers:
Pavel [41]2 years ago
7 0

Answer:

Hey There!

Let's solve...

\frac{a^{3} {b}^{5}  }{ {b}^{4} {a}^{6}  } +   \frac{ {a}^{8} {b}^{6}  }{ {b}^{7} {a}^{9}  } \\  \\  \\  =   \frac{ {a}^{3} { \cancel{b}^{5}} }{{  \cancel{b}^{4}} {a}^{6}  } \\  \\  =  \frac{ {a}^{3}b }{ {a}^{6} } \\  \\  =   \frac{ { \cancel{a}^{3}}b }{  \cancel{{a}^{6}} } \\  =  {a}^{6 - 3} =  {a}^{3}   \\  =  \frac{b}{ {a}^{3} }

Now

\frac{ {a}^{8} {b}^{6}  }{ {b}^{7} {a}^{9}  } \\  \\  \frac{ {a}^{8} }{ {a}^{9} } =  \frac{1}{a} \\  \\ so \: it \: is \:  \frac{ {b}^{6} }{ {b}^{7}a}  \\  \\  \frac{ {b}^{6} }{{b}^{7}  } =  \frac{1}{ba}

So now just make a fraction of them by adding + symbol...

So it will be

\frac{ {b} }{ {a}^{3} } +  \frac{1}{ba} \\  \\

<h2>I hope it is helpful to you...</h2><h3>Cheers!_____________</h3>
vivado [14]2 years ago
3 0

a³b⁵ / b⁴a⁶  ÷ a⁸b⁶ / b⁷a⁹  = 1 / a²

<h3>Indices:</h3>

Indices in math talk about a number raise to another or a variable. They are called exponents.

a³b⁵ / b⁴a⁶  ÷ a⁸b⁶ / b⁷a⁹

Using the law of indices we will simplify the expression as follows;

  • a³b⁵ / b⁴a⁶ =  a³⁻⁶ / b⁵⁻⁴ = a⁻³ / b = 1 / a³b
  • a⁸b⁶ / b⁷a⁹ = a⁸⁻⁹ / b⁶⁻⁷ = a⁻¹ /  b⁻¹ = 1 / ab

Therefore, let's combine the individual simplification.

1 / a³b  ÷ 1 / ab = 1 / a³b × ab / 1

1 / a³b × ab / 1 = 1 / a²

learn more on simplifying indices here: brainly.com/question/10584859?referrer=searchResults

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