Question

Simplify: (8^2/3)^4​

Answer 1

In fraction form, it’s 213333^4/ 10,000^4

Answer 2

Answer:

$(8^{\frac{2}{3} } )^{4} = 256$

Step-by-step explanation:

Given

$(8^{\frac{2}{3} } )^{4}$

Required

Simplify

To simplify this, we apply law of indices but first we start by solving the expression in bracket.

8 =2 * 2 * 2

8 = 2³

So, we substitute 2³ for 8

$(8^{\frac{2}{3} } )^{4}$ becomes

$((2^{3})^{\frac{2}{3} } )^{4}$

From law of indices

$a^{n} = (a^{m})^{\frac{n}{m} }$ ==> $(a^{m})^{\frac{n}{m} } = a^{n}$

So, $(2^{3})^{\frac{2}{3} } = 2^{2}$

At this point we have

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

Also, from law of indices

$(a^{m})^{n} = a^{m.n}$

So,

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

$(2^{2})^{4} = 2^{2*4}$

$(2^{2})^{4} = 2^{8}$

$(2^{2})^{4} = 256$

Hence,

$(8^{\frac{2}{3} } )^{4} = 256$