Question

16^4 x root 16^-1/4

Answer 1

Answer:

We are provided to multply

$16^4 \: by \:\sqrt{16^{-1/4}}$

Now we must know that

→ $a^m \times a^n = a^{m+n}$

:- When a number is multiplied by itself with the any exponent the exponents are added .

→ $a^m \div a^n = a^{m-n}$

:- When a number is divided by itself with the any exponent the exponents are subtracted.

→ $a^{-n} = \dfrac{1}{a^n}$

→$a^{1/n} = \sqrt[n]{a}$

Solution :-

$16^4 \: \times \sqrt{16^{-1/4}}$

$16^4 \times 16^{-1/8}$

$= 16^{4 + (-1/8)}$

$= 16^{4 - \frac{1}{8}}$

$= 16^{\frac{32-1}{8}}$

$= 16^{\frac{31}{8}}$

$= 16^{3}\sqrt[8]{16^7}$