Question

((2c^3*d^4)/(3c^2*d))^2

Probability and combinatorics
ANSWERED
asked 2021-06-01
\(\displaystyle{\left(\frac{{{2}{c}^{{3}}\cdot{d}^{{4}}}}{{{3}{c}^{{2}}\cdot{d}}}\right)}^{{2}}\)

Answers (1)

2021-06-02

We are given: \(\displaystyle{\left(\frac{{{2}{c}^{{3}}\cdot{d}^{{4}}}}{{{3}{c}^{{2}}\cdot{d}}}\right)}^{{2}}\)
Use the rule: \( \frac{a^m}{a^n}=a^m-n =(\frac{(2c^3-2)d^{4-1}}{3})^2 =(\frac{2cd^3}{3})^2\)
Use the rule: \(\displaystyle{\left({a}{b}\right)}^{{n}}={a}^{{n}}\cdot{b}^{{n}}\) and

\((a^m)^n=a^{mn} =\frac{2^2\times c^2\times d^6}{3^{2}} =\frac{4c^2\times d^6}{9}\)

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