Whats 2 to the power of 4 in standard form

Whats 2 to the power of 4 in standard form??

The Correct Answer and Explanation is :

To calculate (2) to the power of (4) (written as (2^4)), we perform the following multiplication:

[
2^4 = 2 \times 2 \times 2 \times 2
]

Breaking it down step by step:

1. First multiplication:
   [
   2 \times 2 = 4
   ]
2. Second multiplication:
   [
   4 \times 2 = 8
   ]
3. Third multiplication:
   [
   8 \times 2 = 16
   ]

So, (2^4 = 16).

Explanation of Exponents

Exponents are a shorthand way of representing repeated multiplication of the same number. In the expression (2^4), the base is (2) and the exponent is (4). This tells us to multiply the base (2) by itself (4) times. The general formula for exponents can be expressed as:

[
a^n = a \times a \times a \times \ldots \text{ (n times)}
]

where (a) is the base and (n) is the exponent. This notation simplifies the representation of large products and is foundational in mathematics.

Standard Form

In mathematics, standard form often refers to writing numbers in a concise manner. For whole numbers like (16), standard form is simply the number itself. However, in the context of scientific notation (a type of standard form), we express numbers as a product of a number between (1) and (10) and a power of (10).

For the number (16):

[
16 = 1.6 \times 10^1
]

Thus, in standard form, (2^4) equals (16), and if needed, it can also be expressed as (1.6 \times 10^1).

In conclusion, (2^4 = 16), which highlights the power of exponents in simplifying mathematical expressions.