Question

1) simplify 2 to the power 2/3 .2 to the power 1/3

2) simplify (root 11 - root 7) (root 11 + root 7)
​

Answer 1

Answer:

$i)2^{\frac{2}{3}}\times 2^{\frac{1}{3}}=2$

$ii)(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})=4$

Step-by-step explanation:

$i) 2^{\frac{2}{3}}\times 2^{\frac{1}{3}}\\=2^{\frac{2}{3}+\frac{1}{3}}$

$Since, \boxed {a^{m}\times a^{n}=a^{m+n}}$

$=2^{\frac{2+1}{3}}\\=2^{\frac{3}{3}}\\=2^{1}\\=2$

Therefore,

$2^{\frac{2}{3}}\times 2^{\frac{1}{3}}=2$

$ii) (\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})\\=(\sqrt{11})^{2}-(\sqrt{7})^{2}$

/* By algebraic identity:

(a-b)(a+b)=a²-b² */

$=11-7\\=4$

Therefore,

$(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})=4$

•••♪