Question

√64=4^n, what is the value of n

Answer 1

Answer:

$\large\boxed{\sf{n=\dfrac{3}{2}}}$

Step-by-step explanation:

From the given question, we have

$\sqrt{64} = {4}^{n}$

Further solving, we get

$= > \sqrt{ {8}^{2} } = {4}^{n} \\ \\ = > { ({8}^{2}) }^{ \frac{1}{2} } = {4}^{n} \\ \\ = > {8}^{(2 \times \frac{1}{2}) } = {4}^{n} \\ \\ = > {8}^{1} = {4}^{n} \\ \\ = > {4}^{n} = 8 \\ \\ = > {( {2}^{2} )}^{n} = {2}^{3} \\ \\ = > {2}^{2n} = {2}^{3}$

Now, bases are same, therefore, exponent must be same.

Therefore, we will get,

$= > 2n = 3 \\ \\ = > \bold{ n = \dfrac{3}{2}}$

Concept Map :-

• ${x}^{m} \times {x}^{n} = {x}^{(m + n)}$

• $\sqrt{ {x}^{2} } = x$

• $\sqrt[m]{x} = {x}^{ \frac{1}{m} }$

• ${ ({x}^{m}) }^{n} = {x}^{mn}$

Answer 2

n=3/2

√64=√4^3

sq root is equal to power raised to 1/2

so √64=(4^3)to the powers1/2

${4 {}^{3} }^{1 \div 2}$

so √64=. { ( a^m)^n= a^mn}

${4}^{3 \div 2}$

so n=3/2

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