Question

Find the value of each of the following expression: $(4 ^{-1})^4 \times 2^5 \times \bigg(\frac{1}{16}\bigg)^3 \times (8^{-2})^5 \times (64^2)^3$

Answer 1

Heya we will transform the following in the powers of two here is your ans.

Because
${a}^{m} \times {a}^{n} = {a}^{m + n}$

Answer 2

Answer:

$2^{-9}$

Step-by-step explanation:

In the question

The given expression is

$(4^{-1})^{4}\times2^{5}\times(\frac{1}{16})^{3}\times(8^{-2})^{5}\times(64^{2})^{3}$

The given expression can be written as

$(2^{2})^{-1\times4}\times2^{5}\times(2^{-4} })^{3}\times(2^{3})^{-2\times5}\times(2^{6})^{2\times3}$

= $2^{2\times-1\times4}\times2^{5}\times2^{-4\times3}\times2^{3\times(-2)\times5}\times2^{6\times2\times3}$

= $2^{-8}\times2^{5}\times2^{-12}\times2^{-30}\times2^{36}$

As we know that

$a^{m}\times a^{n} = a^{m\ +\ n}$

Hence,

$2^{(-\ 8\ +\ 5\ -\ 12\ -\ 30\ +\ 36)}$

= $2^{(-\ 50\ +41)}$

= $2^{-9}$ (Answer)