Simplify in positive index form 0-000729-34- 0-09-34-2-

(0.000729)^ 34× (0.09)^ 34 =(729× 10^ 6× 9× 10^ 2)^ 34 nbsp; [0.5] =(729× 9× 10^ 8)^ 34 =3^6× 3^2× 10^ 8)^ 34 [0.5] =(3^8× 10^ 8)^ 34 =3^8× 34× 10^ 8× 34 ...

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Power & Exponents

Simplify in p...

Question

Simplify in positive index form $(0.000729)^{- \frac{3}{4}} \times (0.09)^{- \frac{3}{4}}$ .
$[2]$

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Solution

$(0.000729)^{- \frac{3}{4}} \times (0.09)^{- \frac{3}{4}}$
$= (729 \times 10^{- 6} \times 9 \times 10^{- 2})^{- \frac{3}{4}}$
$[0.5]$
$= (729 \times 9 \times 10^{- 8})^{- \frac{3}{4}}$
$= 3^{6} \times 3^{2} \times 10^{- 8})^{- \frac{3}{4}}$
$[0.5]$
$= (3^{8} \times 10^{- 8})^{- \frac{3}{4}}$
$= 3^{8 \times - \frac{3}{4}} \times 10^{- 8 \times - \frac{3}{4}}$
$[0.5]$
$= 3^{- 6} \times 10^{6}$
$= \frac{10^{6}}{3^{6}}$
$[0.5]$

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Simplify in positive index form (0.000729)−34×(0.09)−34. [2]

(0.000729)−34×(0.09)−34 =(729×10−6×9×10−2)−34 [0.5] =(729×9×10−8)−34 =36×32×10−8)−34 [0.5] =(38×10−8)−34 =38×−34×10−8×−34 [0.5] =3−6×106 =10636 [0.5]

Simplify in positive index form $(0.000729)^{- \frac{3}{4}} \times (0.09)^{- \frac{3}{4}}$ .
$[2]$