"To calculate: The expression 2.7−11/122.7−1/6 with positive exponent." was answered by students like you

Sinead Mcgee

Answered question

2020-12-13

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

Tasneem Almond

Skilled2020-12-14Added 91 answers

Formula used:
Law of exponent: For any real number a and b and rational exponents m and n for which

a^{m} and a^{n}

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

a^{m / n} exist, the expression a^{- m / n} means \frac{1}{a^{m / n}} .

Calculation:
Consider the given expression

\frac{{2.7}^{- 11 / 12}}{{2.7}^{- 1 / 6}} .

As the above expression have same base. So, use exponent law

\frac{a^{m}}{a^{n}} = a^{m - n},

\frac{{2.7}^{- 11 / 12}}{{2.7}^{- 1 / 6}} = {2.7}^{- 11 / 12 - (- 1 / 6)}

As, the denominator of exponent is same, so,

{2.7}^{- 11 / 12 - (- 1 / 6) = {2.7}^{- 11 / 12 - (- 2 / 6)}}

= {2.7}^{- 9 / 12}

= {2.7}^{- 3 / 4}

So, by reciprocating the base value of negative exponent,

{2.7}^{- 3 / 4} = \frac{1}{{2.7}^{3 / 4}}

Thus, the value of expression

\frac{{2.7}^{- 11 / 12}}{{2.7}^{- 1 / 6}} i s \frac{1}{{2.7}^{3 / 4} .}

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