If 2^{x} × 8^{\;1/5} = 2^{\;1/5}, then the value of x is

Correct Answer is : − 25-\;2/5−52

Correct Answer is : − 25-\;2/5−52

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Question : 72 of 86

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2^{x} \times 8^{\;\frac{1}{5}} = 2^{\;\frac{1}{5}}

x

Solution:

Concept:

Use laws of indices to equate exponents after expressing all terms with the same base.

Explanation:

Given:

2^{x} \times 8^{\frac{1}{5}} = 2^{\frac{1}{5}}

Write

8

2^3

, so

8^{\frac{1}{5}} = (2^3)^{\frac{1}{5}} = 2^{\frac{3}{5}}

Then the equation becomes

2^{x} \times 2^{\frac{3}{5}} = 2^{\frac{1}{5}}

Using

a^m \times a^n = a^{m+n}

, we get

2^{x + \frac{3}{5}} = 2^{\frac{1}{5}}

Since bases are equal, equate exponents:

x + \frac{3}{5} = \frac{1}{5}

Thus

x = \frac{1}{5} - \frac{3}{5} = -\frac{2}{5}

Answer:

x = -\frac{2}{5}

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