Question

2x to the power 1/6*2x to the power -7/6

Answer 1

$2x {}^{ \frac{1}{6} } \times 2x {}^{ \frac{ - 7}{6} } \\ = (2 \times 2) \times x {}^{ \frac{1}{6} + ( \frac{ - 7}{6}) } \\ = 4 \times x {}^{ \frac{1 - 7}{6} } \\ = 4 \times x {}^{ \frac{ - 6}{6} } \\ = 4 \times x {}^{ - 1} \\ = 4 \times \frac{1}{x} \\ = \frac{4}{x}$
Hope this will help you

Answer 2

Answer:

$\frac{1}{2x}$

Step-by-step explanation:

The given expression is

$(2x)^{\frac{1}{6}}\times (2x)^{-\frac{7}{6}}$

We need to find the simplified form of the given expression.

According to the product property of exponent.

$a^ma^m=a^{m+n}$

Using product property of exponent, the given expression can be rewritten as

$(2x)^{\frac{1}{6}+(-\frac{7}{6})}$

$(2x)^{\frac{1}{6}-\frac{7}{6}}$

$(2x)^{\frac{-6}{6}}$

$(2x)^{-1}$

Using the property of exponent, we get

$\frac{1}{2x}$                    $[\because a^{-n}=\frac{1}{a^n}]$

Therefore, value of given expression is $\frac{1}{2x}$.