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5/9 power -2 * 3/5 power -3 * 3/5 power 0

Sagot :

msvivinguyen

Answer:

15

Step-by-step explanation:

5/9^-2 = 81/25

3/5^-3 = 125/27

3/5^0 = 1

81/25 x 512/27 x 1 = 15

devishri1977

Answer:

15

Step-by-step explanation:

Exponent law:

  [tex]\boxed{\left(\dfrac{a}{b}\right)^{-m}=\left(\dfrac{b}{a}\right)^m}\\\\\boxed{\dfrac{a^m}{a^n}=a^{m-n}}\\\\\boxed{(a^{m})^n=a^{m*n}}[/tex]

[tex]\sf \left(\dfrac{5}{9}\right)^{-2}*\left(\dfrac{3}{5}\right)^{-3}*\left(\dfrac{3}{5}\right)^0=\left(\dfrac{5}{9}\right)^{-2}*\left(\dfrac{3}{5}\right)^{-3}*1\\\\ \text{Any variable or number raised to 0 =1} \\[/tex]

   

                                         [tex]= \left(\dfrac{9}{5}\right)^2*\left(\dfrac{5}{3}\right)^3}\\\\= \dfrac{(3^2)^2}{5^2}*\dfrac{5^3}{3^3}\\\\=\dfrac{3^{2*2}}{5^2}}*\dfrac{5^3}{3^3}\\\\=\dfrac{3^{4}}{5^{2}}*\dfrac{5^3}{3^3}\\\\=3^{4-3}*5^{3-2}\\\\=3^1*5^{1}\\\\=15[/tex]                      

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