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belka [17]
4 years ago
10

Please someone answer this please

Mathematics
1 answer:
gladu [14]4 years ago
8 0

Option C:

\frac{3 a^{2} b^{11}}{2 } is equivalent to the given expression.

Solution:

Given expression:

$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}

To find which expression is equivalent to the given expression.

$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}

Using exponent rule: \frac{1}{a^m}=a^{-m}, \ \  \frac{1}{a^{-m}}=a^{m}

    $=\frac{-18 a^{-2} b^{5}a^{4} b^{6}}{-12 }

    $=\frac{-18 a^{-2} a^{4} b^{5} b^{6}}{-12 }

Using exponent rule: {a^m}\cdot{a^n}=a^{m+n}

    $=\frac{-18 a^{(-2+4)} b^{(5+6)}}{-12 }

   $=\frac{-18 a^{2} b^{11}}{-12 }

Divide both numerator and denominator by the common factor –6.

   $=\frac{3 a^{2} b^{11}}{2 }

$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}=\frac{3 a^{2} b^{11}}{2 }

Therefore, \frac{3 a^{2} b^{11}}{2 } is equivalent to the given expression.

Hence Option C is the correct answer.

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