Question

Write 2^8 * 8^2 * 4^-4 in the form 2^n

Answer 1

The given expression 2^8 * 8^2 * 4^-4 can be written in the exponential form 2^n as 2^6.

What are exponential forms?

The exponential form is a more convenient way to write repetitive multiplication of the same integer by using the base and its exponents.

For example:

If we have a*a*a*a, it can be written in exponential form as:

=a^4

where

• a is the base, and
• 4 is the power.

The power in this format reflects the number of times we multiply the base by itself. The exponent is also known as the index or power. 

From the information given:

We can write 2^8 * 8^2 * 4^-4 in form of 2^n as follows:

$\mathbf{= 2^8\times (2^3)^2 \times (2^2)^{-4} }$

$\mathbf{= 2^8\times (2^6) \times (2^{-8}) }$

$\mathbf{= 2^{8+6+(-8)}}$

$\mathbf{= 2^{6}}$

Therefore, we can conclude that by using the exponential form, the given expression 2^8 * 8^2 * 4^-4 in the form 2^n is 2^6.

Learn more about exponential forms here:

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