Question

Simplify the expression. 64 7/12 16 8 √2 4√2 32

Answer 1

Answer:

$8\sqrt2$

Second option is correct.

Step-by-step explanation:

We have been given the expression $(64)^{\frac{7}{12}}$

We can write the term 64 as $64=2^6$

Thus, we have

$(2^6)^{\frac{7}{12}}$

Now, use the exponent law $(x^m)^n=x^{mn}$

$(2)^{6\cdot\frac{7}{12}}$

On simplifying, we get

$(2)^{\frac{7}{2}}$

This expression can be further simplified as

$\sqrt{2^7}\\\\=\sqrt{2^6\cdot2}\\\\=2^3\sqrt{2}\\\\=8\sqrt2$

Second option is correct.