"To calculate: To evaluate the expression (27x6y3)−23." was answered by our community

Emeli Hagan

Answered question

2021-11-03

To calculate:
To evaluate the expression

{(27 x^{6} y^{3})}^{- \frac{2}{3}}

Bentley Leach

Skilled2021-11-04Added 109 answers

Calculation:
Applying the fraction rule,

\frac{- a}{b} = - \frac{a}{b}

The expression can be written as

{(27 x^{6} y^{3})}^{- \frac{2}{3}}

According to the basic rules of exponents,

a^{- m} = \frac{1}{a^{m}}

Applying the above rule,
This can be written as

\frac{1}{{(27 x^{6} y^{3})}^{\frac{2}{3}}}

{(27 x^{6} y^{3})}^{\frac{2}{3}} = 27^{\frac{2}{3}} {(x^{6})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}

(According to exponent rule,

{(a \cdot b)}^{n} = a^{n} b^{n})

\frac{1}{{(27 x^{6} y^{3})}^{\frac{2}{3}}} = \frac{1}{27^{\frac{2}{3}} {(x^{6})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}

\frac{1}{{(27 x^{6} y^{3})}^{\frac{2}{3}}} = \frac{1}{{(3^{3})}^{\frac{2}{3}} {(x^{6})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}

\frac{1}{{(27 x^{6} y^{3})}^{\frac{2}{3}}} = \frac{1}{{(3)}^{3 \times \frac{2}{3}} {(x)}^{6 \times \frac{2}{3}} {(y)}^{3 \times \frac{2}{3}}}

\frac{1}{{(27 x^{6} y^{3})}^{\frac{2}{3}}} = \frac{1}{9 x^{4} y^{2}}

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