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Choose the correct simplification of [tex] \frac{a^5b^6}{a^4b^4} [/tex]

(a) [tex] a^9b^1^0 [/tex]
(b) [tex] ab^2 [/tex]
(c) [tex] \frac{1}{ab^2} [/tex]
(d) [tex] \frac{1}{a^9b^1^0} [/tex]

Respuesta :

The correct simplification will be: (b) ab²

[tex] \frac{a^5 b^6}{a^4 b^4} [/tex]

Here we will use the property of exponents for division of two exponential terms with same bases. The original property is : [tex] \frac{x^m}{x^n} = x^m^-^n [/tex]

It means if the bases are same , then we will just subtract the exponents while dividing two terms.

Using this property:

[tex] \frac{a^5}{a^4} = a^5^-^4 = a^1 = a [/tex]

and [tex] \frac{b^6}{b^4} = b^6^-^4 = b^2 [/tex]

So, [tex] \frac{a^5 b^6}{a^4 b^4}
= ab^2 [/tex]

Answer:

a^5 - a^4 = a1 or a

b^6 - b^4 = b2

put them together and you get ab^2

I also took the test and got it right

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