Question

Which function has a simplified base of 4 ^3 sqrt 4?

Answer 1

Answer:

Step-by-step explanation:

To find the function with simplified base, we change every composite no into prime no. by factorizing them and rewriting in exponential form.

Given: function $4^3\times\sqrt{4}$

Here 4 is only composite no in base.

∴ the expontial form of 4 = $2^2$

putting it in given function we get,

$(2^2)^3\times\sqrt{2^2}$

⇒ $2^{2\times3}\times 2$ ( ∵ acc. to law of exponent, $(a^b)^c=a^b\timesc$ )

⇒$2^6\times2^1$

⇒$2^{6+1}$ ( ∵ acc. to law of exponent, $x^a\times x^b=x^{a+b}$ )

⇒$2^7$

⇒ 2×2×2×2×2×2×2

⇒ 128

Answer 2

We have
$4^{3} * \sqrt{4}$

We start by calculating square root:
$4^{3} *2$

We can rewrite 4 in base of 2:
$( 2^{2}) ^{3}*2$

Now we can calculate this by using rule of same base and different exponent:
$2^{6}*2^{1} =2^{7} =128$