$2x^2\times y^2\times 2z^2\times 3y^2\times 4x^2$

১। সরল কর:

$$\begin{gathered} \left(i\right)x^3\times x^7 \\ \left(ii\right)a^3\times a\times a^5 \\ \left(iii\right)x^4\times x^2\times x^9 \\ \left(iv\right)m\times m^2\times n^3\times m^3\times n^7 \\ \left(v\right)3a\times 4b\times 2a\times 5c\times 3b \\ \left(vi\right)2x^2\times y^2\times 2z^2\times 3y^2\times 4x^2 \end{gathered}$$

২। a = 2 b = 3 c = 1 হলে, নিচের রাশিগুলোর মান নির্ণয় কর:

$$\begin{gathered} \left(i\right)a^3+b^2 \\ \left(ii\right)b^3+c^3 \\ \left(iii\right)a^2-b^2+c^2 \\ \left(iv\right)b^2-2ab+a^2 \\ \left(v\right)a^2-2ac+c^2 \end{gathered}$$

৩। x = 3 y = 5 z = 2 হলে, দেখাও যে,

$$\begin{gathered} \left(i\right)y^2-x^2=(x+y)(y-x) \\ \left(ii\right)(x+y{)}^2=(x-y{)}^2+4xy \\ \left(iii\right)(y+z{)}^2=y^2+2yz+z^2 \\ (iv\left)\right(x+z{)}^2=x^2+2xz+z^2 \end{gathered}$$

৪। সঠিক উত্তরটি লেখ:

(i) $a^7\times a^8$ এর মান কোনটি?

$$\begin{gathered} \left(ক\right)a^{56} \\ \left(খ\right)a^{15} \end{gathered}$$
(গ) 15
(ঘ) 56

(ii) $a^3\times a^{-3}$ এর মান কোনটি?

$$\begin{gathered} \left(ক\right)a^6 \\ \left(খ\right)a^9 \\ \left(গ\right)a^0 \\ \left(ঘ\right)a^3 \end{gathered}$$

(iii) $5x^2\times 4x^4$ এর মান কোনটি?

$$\begin{gathered} \left(ক\right)x^6 \\ \left(খ\right)20x^6 \\ \left(গ\right)20x^8 \\ \left(ঘ\right)9x^6 \end{gathered}$$

(iv) $x^5\times x^4এ x$ এর সূচক কোনটি?

$$\begin{gathered} \left(ক\right)x^{20} \\ \left(খ\right)x^9 \\ \left(গ\right)9 \\ \left(ঘ\right)20 \end{gathered}$$

(v) $5a^3 \times a^{5 }এ a$ এর সূচক কোনটি?

(ক) 5
(খ) a⁸
(গ) 15
(ঘ) ৪