Question

Express 256 as a power of 4.

Answer 1

Define exponents and state given data

Exponent:

• The way of expressing large numbers in terms of the powers of their factors is known as exponents.
• For example, the number $64$ can be written as an exponent as $64=2\times 2\times 2\times 2\times 2\times 2=2^6$.

The given number is $256$.

Find the prime factors and express them as the power of $\mathbf{4}$

The given number $256$ can be expressed in terms of its prime factors as follows,

$\because 256=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

Converting the factors into $4$ by multiplying $2s$ together,

$$\begin{gathered} 256=4\times 4\times 4\times 4 \\ \Rightarrow 256=4^4 \end{gathered}$$

Hence, $256$ can be expressed as a power of $4$ as $256=4^4$.