Question

Please answer this question.​

Answer 1

Answer:

x= -2

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Answer 2

Answer:

-2

Step-by-step explanation:

The given expression is

$( \frac{ - 1}{3} )^{ - 6} \times (\frac{ - 1}{3} )^{5} = { (\frac{ - 1}{3} )}^{x + 1}$

We have to find the value of x.

$\large\underline{\sf{We \: know \: that, }}$

$\large\underline{\sf{ {a}^{m} \times {a}^{n} = {a}^{m+n} }}$

$\large\underline{\sf{So,}}$

$\large\underline{\sf{( \frac{ - 1}{3} )^{ - 6} \times ( \frac{ - 1}{3} ) ^{5} }}$

$\large\underline{\sf{It \: can \: be \: written \: as}}$

$\large\underline{\sf{( \frac{ - 1}{3})^{ - 6 + 5} = ( \frac{ - 1}{3} ) ^{x + 1} }}$

$\large\underline{\sf{( \frac{ - 1}{3})^{ - 1} = ( \frac{ - 1}{3} ) ^{x + 1} }}$

$\large{\sf{Using \: transportation \: method}}$

$\large\underline{\sf{( \frac{ - 1}{3})^{ - 1 - 1} = (\frac{ - 1}{3}) ^{x} }}$

$\large\underline{\sf{( \frac{ - 1}{3} )^{ - 2} = (\frac{ - 1}{3}) ^{x} }}$