Question

Write in scientific notation: \[{(400000)^4}\]
A) \[6.4 \times {10^{20}}\]
B) \[2.56 \times {10^{20}}\]
C) \[2.56 \times {10^{22}}\]
D) \[6.4 \times {10^{19}}\]

Answer 1

Hint:Scientific notation is a way of writing down very large or very small numbers easily.
The rules when writing a number in scientific notation is that first you write down a number between \[1\] and \[10\], then you multiply it by \[10\] to the power of a number.
Scientific notation \[ = m \times {10^n}\] where, \[1 \leqslant m < 10\].

Complete step-by-step answer:
The given number is \[{(400000)^4}\]. We need to write the number in scientific notation.
We know that, if we need to write one number in scientific notation then we first need to write a number between \[1\] and \[10\] then multiply it by \[10\] to the power of a number.
Thus, \[{(400000)^4} = {4^4} \times {(100000)^4} = 256 \times {\{ {(10)^5}\} ^4} = 256 \times {10^{20}}\]
So, for expressing \[256 \times {10^{20}}\] in the scientific notation we first need to write a number between \[1\] to \[10\] then multiply it by \[10\] to the power of a number.
That is, we can express \[256 \times {10^{20}}\] as \[2.56\] multiplied by \[10\] to the power \[22\].
\[ \Rightarrow 256 \times {10^{20}} = 2.56 \times {10^{22}}\]
Therefore we get,
Scientific notation of \[{(400000)^4}\] is \[2.56 \times {10^{22}}\].

So, the correct answer is “Option C”.

Note:Scientific notation is a way of expressing real numbers that are too large or too small to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the UK.
Small numbers can also be written in scientific notation. However, instead of the index being positive (in the above example in hint, the index was \[3\]), it will be negative. The rules when writing a number in scientific notation is that first you write down a number between \[1\] to\[10\] , then you multiply it by \[10\] to the power of a number.
We have used here, \[{({a^m})^n} = {a^{m.n}} = {a^{mn}}\].