# To calculate:The expression (2.7^(-11/12))/(2.7^(-1/6)) with positive exponent.

To calculate:
The expression $\frac{{2.7}^{-11\text{/}12}}{{2.7}^{-1\text{/}6}}$ with positive exponent.

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Tasneem Almond
Formula used:
Law of exponent: For any real number a and b and rational exponents m and n for which are defined, when deviding, exponents are subtracted for same base, that is,
$\frac{{a}^{m}}{{a}^{n}}={a}^{m-n}$
Negative rational exponents:
For any non-zero number a for which
Calculation:
Consider the given expression $\frac{{2.7}^{-11\text{/}12}}{{2.7}^{-1\text{/}6}}.$
As the above expression have same base. So, use exponent law $\frac{{a}^{m}}{{a}^{n}}={a}^{m-n},$
$\frac{{2.7}^{-11\text{/}12}}{{2.7}^{-1\text{/}6}}={2.7}^{-11\text{/}12-\left(-1\text{/}6\right)}$
As, the denominator of exponent is same, so,
${2.7}^{-11\text{/}12-\left(-1\text{/}6\right)={2.7}^{-11\text{/}12-\left(-2\text{/}6\right)}}$
$={2.7}^{-9\text{/}12}$
$={2.7}^{-3\text{/}4}$
So, by reciprocating the base value of negative exponent,
${2.7}^{-3\text{/}4}=\frac{1}{{2.7}^{3\text{/}4}}$
Thus, the value of expression $\frac{{2.7}^{-11\text{/}12}}{{2.7}^{-1\text{/}6}}is\frac{1}{{2.7}^{3\text{/}4}.}$