Question

radical form of 27^1/5​

Answer 1

Answer:

$\sqrt[5]{27}$

Hope it helps

Step-by-step explanation:

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Answer 2

Answer:

Required radical form of ${27}^{ \frac{1}{5} }$is ${3}^{ \frac{3}{5} }$

Step-by-step explanation:

Given,

${27}^{ \frac{1}{5} }$

This is a problem of power of indices.

Here need to breck 27 into prime numbers.

So,

$27 = 3 \times 3 \times 3 = {3}^{3}$

Now,

${27}^{ \frac{1}{5} } = {3}^{ {3}^{ \frac{1}{5} } } = {3}^{3 \times \frac{1}{5} } = {3}^{ \frac{3}{5} }$

Required radical form of ${27}^{ \frac{1}{5} }$is ${3}^{ \frac{3}{5} }$

Here applied formula is ${x}^{ {y}^{a} } = {x}^{ya}$

Some other important formulas of power of indices

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$