Question

Consider the equation: ((1/(27 × 81))³)⁴ = 1/3ᵖ Find the value of p.​

Answer 1

Step-by-step explanation:

$\begin{gathered} \rm\dfrac{ {27}^{ - \frac{2}{3} } \times {81}^{ \frac{5}{4} } }{ ({ \dfrac{1}{3}) }^{ - 3} } \\ = \frac{ {( {3}^{3} )}^{ -\frac{2}{3} } \times {( {3}^{4} )}^{ \frac{5}{4} } }{ \frac{1}{ {3}^{ - 3} } } \\ = \frac{ {3}^{ - 2} \times {3}^{5} }{ {3}^{3} } \\ = {3}^{ - 2} \times {3}^{5} \times {3}^{ - 3} \\ = {3}^{ - 2 + 5 - 3} \\ = {3}^{0} \\ = 1\end{gathered}$

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