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Simplify the following. Is the constant term in the numerator or denominator?

Simplify the following. Is the constant term in the numerator or denominator?-example-1
User Tunmee
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1 Answer

1 vote

Answer:

Numerator.

Explanation:

(2a¯⁵b²/ab³)¯³

To know if the constant term will be in the numerator or denominator, let us simplify the expression. This can be obtained as follow:

(2a¯⁵b²/ab³)¯³

Recall

m¯ⁿ = 1/mⁿ

Therefore,

(2a¯⁵b²/ab³)¯³ = 1/(2a¯⁵b²/ab³)³

= 1 ÷ (2a¯⁵b²/ab³)³

= 1 × (ab³ / 2a¯⁵b²)³

= (ab³ / 2a¯⁵b²)³

Recall

(mⁿ)ˣ = mⁿˣ

Therefore,

(ab³ / 2a¯⁵b²)³ = a³b⁹ / 2³a¯¹⁵b⁶

Recall

x^m ÷ x^n = x^(m–n)

Therefore,

a³b⁹ / 2³a¯¹⁵b⁶ = a^(3 - - 15)b^(9-6)/2³

= a^(3 +15) b^(9-6)/2³

= a¹⁸b³/2³

Thus,

(2a¯⁵b²/ab³)¯³ = a¹⁸b³/2³

From the above illustration, we can see that the constant term (i.e 'a' and 'b') are in the numerator.

User Raunaq Kochar
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