Question

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

Answer 1

15

Explanation:

5/9^-2 = 81/25

3/5^-3 = 125/27

3/5^0 = 1

81/25 x 512/27 x 1 = 15

Answer 2

15

Explanation:

Exponent law:

`\boxed{\left((a)/(b)\right)^(-m)=\left((b)/(a)\right)^m}\\\\\boxed{(a^m)/(a^n)=a^(m-n)}\\\\\boxed{(a^(m))^n=a^(m*n)}`

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

`= \left((9)/(5)\right)^2*\left((5)/(3)\right)^3}\\\\= ((3^2)^2)/(5^2)*(5^3)/(3^3)\\\\=(3^(2*2))/(5^2)}*(5^3)/(3^3)\\\\=(3^(4))/(5^(2))*(5^3)/(3^3)\\\\=3^(4-3)*5^(3-2)\\\\=3^1*5^(1)\\\\=15`