Question

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Answer 1

Step-by-step explanation:

For explanation, please see the picture above.

Answer 2

Question:

$\dfrac{ {4}^{64} }{ {64}^{4}} = {( {4}^{4}) }^{k}$

Find the value of k.

Answer:

$\large\boxed{\sf{k=13}}$

Step-by-step explanation:

From the given question, we have

$= > \dfrac{ {4}^{64} }{ {64}^{4} } = {( {4}^{4} )}^{k}$

We know that,

• ${ ({a}^{m} )}^{n} = {a}^{ mn}$

Therefore, we will get,

$= > \dfrac{ {4}^{64} }{ {( {4}^{3} )}^{4} } = {4}^{4k} \\ \\ = > \frac{ {4}^{64} }{ {4}^{12} } = {4}^{4k}$

Also, we know that,

• $\dfrac{ {x}^{m} }{ {x}^{n} } = {x}^{m - n}$

Therefore, we will get,

$= > {4}^{4k} = {4}^{(64 - 12)} \\ \\ = > {4}^{4k} = {4}^{52}$

Now, bases are same, therefore, exponents will also be same.

Therefore, we will get,

$= > 4k = 52 \\ \\ = > k = \dfrac{52}{4} \\ \\ = > k = 13$

Hence, k = 13