plz simplify with steps

[tex] \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} } [/tex]

Now

[tex] \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} [/tex]

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

So it will be

[tex] \frac{ {b} }{ {a}^{3} } + \frac{1}{ba} \\ \\ [/tex]

I hope it is helpful to you...

Cheers!_____________

vintechnology vintechnology · Answer 2 · 2022-01-26T18:33:45+01:00

a³b⁵ / b⁴a⁶ ÷ a⁸b⁶ / b⁷a⁹ = 1 / a²

Indices:

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: https://brainly.com/question/10584859?referrer=searchResults