Question

Please help simplify the following expression

Answer 1

Answer:

$7 m^{21}n^{66}p^{5}$

Step-by-step explanation:

Given expression:

$\dfrac{21m^{42}n^{82}p^{10}}{3m^{21}n^{16}p^{5}}$

Therefore:

$\implies \dfrac{21}{3} \cdot \dfrac{m^{42}}{m^{21}} \cdot \dfrac{n^{82}}{n^{16}} \cdot \dfrac{p^{10}}{p^5}$

Simplify the coefficient:

$\implies 7 \cdot \dfrac{m^{42}}{m^{21}} \cdot \dfrac{n^{82}}{n^{16}} \cdot \dfrac{p^{10}}{p^5}$

$\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:$

$\implies 7 \cdot m^{42-21} \cdot n^{82-16} \cdot p^{10-5}$

$\implies 7 \cdot m^{21} \cdot n^{66} \cdot p^{5}$

Therefore:

$\implies 7 m^{21}n^{66}p^{5}$

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