Question

3√4 × 3√16 = .......................

Answer 1

ANSWER

Given, 3√4 × 3√16

Now according to laws of Exponents or laws of Indices, we have =>

$\mathrm{Now,\:3\sqrt{4} * 3\sqrt{16}}$

$\mathrm{= 3*4^{\frac{1}{2}}*3*16^{\frac{1}{2}}}$

$\mathrm{= 3*(2^{2})^{\frac{1}{2}}*3*(4^{2})^{\frac{1}{2}}}$

$\mathrm{= 3*2^{\frac{2}{2}}*3*4^{\frac{2}{2}}}$

$\mathrm{= 3 * 2^{1} * 3 * 4^{1}}$

$\mathrm{= 3 * 2 * 3 * 4}$

$\bold{= 72}$

$\to \boxed{\bold{3\sqrt{4} * 3\sqrt{16}=72}}$

REMEMBER

Laws of Indices

1)$a^n$ × $a^m$=$a^{m+n}$

2)$a^m$ ÷ $a^n$= $a^{m-n}$

3)$(a^{m})^{n}=a^{mn}$

4)$a^0$ = 1

5) $(\dfrac{a}{b})^n$ = $\dfrac{{a}^n}{{b}^n}$

6)$a^{-1}$ = $\dfrac{1}{a}$

Answer 2

Hope it helps u☺☺☺☺☺☺☺☺☺