Question

Simplify open parentheses x to the 2 ninths power close parentheses to the 3 eighths power.

Answer 1

Answer:

Option 2

$(x^{\frac{2}{9}})^{\frac{3}{8}}=x^{\frac{1}{12}}$

Step-by-step explanation:

Given : Open parentheses x to the 2 ninths power close parentheses to the 3 eighths power.

To find : Simplify the given expression?

Solution :

Open parentheses x to the 2 ninths power close parentheses to the 3 eighths power i.e, $(x^{\frac{2}{9}})^{\frac{3}{8}}$

Applying the power rule of exponent, $(x^a)^b=x^{a\cdot b}$

$(x^{\frac{2}{9}})^{\frac{3}{8}}$

$=x^{\frac{2}{9}\times\frac{3}{8}}$

$=x^{\frac{2\times 3}{9\times 8}}$

$=x^{\frac{6}{72}}$

$=x^{\frac{1}{12}}$

Therefore, Option 2 is correct.

$(x^{\frac{2}{9}})^{\frac{3}{8}}=x^{\frac{1}{12}}$

Answer 2

The given expression is

$(x^{2/9})^{3/8}$

Here we have two exponents, so we have to use power of a power rule of exponent , in which we need to multiply the exponents . And on doint this, we will get

$x^({2/9}*{3/8}) =x^{6/72} = x^{1/12}$

And it is equal to x to the 1 twelfth power. SO the correct option is the second option .