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hoa [83]
2 years ago
12

Need the a answer for this

Mathematics
1 answer:
FinnZ [79.3K]2 years ago
4 0

Answer:

Given expression:

\dfrac{14a^4b^6c^{-10}}{8a^{-2}b^3c^{-5}}

Separate the variables:

\implies \dfrac{14}{8} \cdot \dfrac{a^4}{a^{-2}} \cdot \dfrac{b^6}{b^3} \cdot \dfrac{c^{-10}}{c^{-5}}

Reduce the first fraction:

\implies \dfrac{7}{4} \cdot \dfrac{a^4}{a^{-2}} \cdot \dfrac{b^6}{b^3} \cdot \dfrac{c^{-10}}{c^{-5}}

\textsf{Apply Division Property of Exponents rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:

\implies \dfrac{7}{4} \cdot a^{4-(-2)} \cdot b^{6-3} \cdot c^{-10-(-5)}

\implies \dfrac{7}{4} \cdot a^{6} \cdot b^{3} \cdot c^{-5}

\textsf{Apply Negative Property of Exponents rule} \quad a^{-n}=\dfrac{1}{a^n}

\implies \dfrac{7}{4} \cdot a^{6} \cdot b^{3} \cdot \dfrac{1}{c^5}

Therefore:

\implies \dfrac{7a^6b^3}{4c^5}

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