Question

express 4^-5 as a power with base 2 ? Why give reason...​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The final answer is  $2^{-10}$. $4^{-5}$  can be expressed as an exponent with base 2 and power -10 which is $2^{-10}$.

Step-by-step explanation:

Given that,

$4^{-5}$ is a number with base 4 and power -5.

Now, we have to change the base of this number from 4 to 2.

As we know,

4 can be represented in terms of base 2.

So, 4 = 2 × 2 = $2^2$

4 is the number with a base of 2 and a power of 2.

By replacing 4 with $2^2$ in the number we get,

$4^{-5}$ = $(2^2)^{-5}$

As we know from the laws of exponents, $(a^m)^{n} = a^{mn}$

So, here m = 2 and n = -5

By multiplying the powers, we get m × n = 2 × -5 = -10

Now, $4^{-5}$ = $(2^2)^{-5}$ = $2^{-10}$

So, $4^{-5}$  can be represented as a number with base 2 and power -10 which is $2^{-10}$.

Therefore, $4^{-5}$  can be expressed as an exponent with base 2 and power -10 which is $2^{-10}$.

To know more about exponents, visit the link below:

https://brainly.in/question/54086809

To know more about the laws of exponents, visit the links below:

https://brainly.in/question/25724

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