Question

Q1.Simplify:

(I) {1³+2³}×(1/3) ²
(II) {5^-1×4^-1}²
(III) {(1/3) ^-1×(1/2)^-2}÷(1/4) ^-3

Give correct answer I will mark as brianlist. It wrong will deleated.

Answer 1

`\textbf{(i)}\\\\\{1^3 +2^3 \} * \left(\frac 13 \right)^2\\\\=(1+8) \left(\frac 19 \right)\\\\=9\left(\frac 19 \right)\\\\=1\\\\`

`\textbf{(ii)}\\\\\{5^(-1)* 4^(-1)\}^2\\\\=\left(5^(-1) \right)^2 * \left(4^(-1) \right)^2~~~~~~~~~~~;[(ab)^m = a^mb^m]\\\\=5^(-2)* 4^(-2)~~~~~~~~~~~~~~~~~~~~;[(a^m)^n = a^(mn)]\\\\=\frac 1{5^2} * \frac 1{4^2}~~~~~~~~~~~~~~~~~~~~~~;\left[a^(-m) = \frac 1{a^m},~ a\\eq 0 \right]\\\\=(1)/(400)\\\\=0.0025\\\\`

`\textbf{(iii)}\\\\\left\{ \left(\frac 13 \right)^(-2) * \left( \frac 12 \right)^(-2)\right\}/ \left(\frac 14 \right)^(-3)\\\\\\=\left( \frac 13 * \frac 12 \right)^(-2) /\left(4^(-1)\right)^(-3)\\\\\\=\left(\frac 16 \right)^(-2) / 4^3\\\\\\=\left(6^(-1) \right)^(-2)/ 4^3\\\\\\=6^2 / 4^3\\\\\\=36/ 64\\\\\\=(9)/(16)\\\\\\=0.5625`