Sinead Mcgee

2020-12-13

To calculate:

The expression

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

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

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

As, the denominator of exponent is same, so,

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

$={2.7}^{-9\text{/}12}$

$={2.7}^{-3\text{/}4}$

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$\frac{{2.7}^{-11\text{/}12}}{{2.7}^{-1\text{/}6}}is\frac{1}{{2.7}^{3\text{/}4}.}$

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

Negative rational exponents:

For any non-zero number a for which

Calculation:

Consider the given expression

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

As, the denominator of exponent is same, so,

So, by reciprocating the base value of negative exponent,

Thus, the value of expression

22+64

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