Question

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

Rational exponents and radicals
ANSWERED
asked 2020-12-13
To calculate:
The expression \(\displaystyle\frac{{2.7}^{{-{11}\text{/}{12}}}}{{2.7}^{{-{1}\text{/}{6}}}}\) with positive exponent.

Answers (1)

2020-12-14
Formula used:
Law of exponent: For any real number a and b and rational exponents m and n for which \(a^{m}\ \text{and}\ a^{n}\) are defined, when deviding, exponents are subtracted for same base, that is,
\(\displaystyle\frac{{a}^{m}}{{a}^{n}}={a}^{{{m}-{n}}}\)
Negative rational exponents:
For any non-zero number a for which \(\displaystyle{a}^{{{m}\text{/}{n}}}\ \text{exist, the expression}\ \displaystyle{a}^{{-{m}\text{/}{n}}}\ \text{means}\ \displaystyle\frac{1}{{a}^{{{m}\text{/}{n}}}}.\)
Calculation:
Consider the given expression \(\displaystyle\frac{{2.7}^{{-{11}\text{/}{12}}}}{{2.7}^{{-{1}\text{/}{6}}}}.\)
As the above expression have same base. So, use exponent law \(\displaystyle\frac{{a}^{m}}{{a}^{n}}={a}^{{{m}-{n}}},\)
\(\displaystyle\frac{{2.7}^{{-{11}\text{/}{12}}}}{{2.7}^{{-{1}\text{/}{6}}}}={2.7}^{{-{11}\text{/}{12}-{\left(-{1}\text{/}{6}\right)}}}\)
As, the denominator of exponent is same, so,
\(\displaystyle{2.7}^{{-{11}\text{/}{12}-{\left(-{1}\text{/}{6}\right)}={2.7}^{{-{11}\text{/}{12}-{\left(-{2}\text{/}{6}\right)}}}}}\)
\(\displaystyle={2.7}^{{-{9}\text{/}{12}}}\)
\(\displaystyle={2.7}^{{-{3}\text{/}{4}}}\)
So, by reciprocating the base value of negative exponent,
\(\displaystyle{2.7}^{{-{3}\text{/}{4}}}=\frac{1}{{{2.7}^{{{3}\text{/}{4}}}}}\)
Thus, the value of expression \(\displaystyle\frac{{2.7}^{{-{11}\text{/}{12}}}}{{2.7}^{{-{1}\text{/}{6}}}}{i}{s}\frac{1}{{{2.7}^{{{3}\text{/}{4}}}.}}\)
0
 
Best answer

expert advice

Need a better answer?
...