Question

(16/81) to the power of (-3/4) is equal to​

Answer 1

Answer:

Let's start by getting your terminology right. There is no variable here, so there is nothing to solve for. What you are intending to ask is, “How do I ‘simplify’ this expression”.

The order of operations can be done multiple ways on this one. I like to start by recognizing the negative symbol in the exponent as a “reciprocal sign”.

So  1681−34  =811634 .

(Technically these fractions should be in parentheses but I'm having a time getting the MathType to cooperate.)

Next, recognizing that the 4 in the denominator of the rational exponent means to take the 4th root, I do that next.

1614=2  and  8114=3  

So now I have:

(32)3=278  

Answer 2

Answer:

${ \frac{16 }{81} }^{ \frac{ - 3}{4} } \\ = {( { \frac{2}{3} }^{4} )}^{ \frac{ - 3}{4} } = { \frac{2}{3} }^{4 \times \frac{ - 3}{4} } \\ = { \frac{2}{3} }^{ - 3} = { \frac{3}{2} }^{3} \\ = \frac{27}{8} \\ = 3 \frac{3}{8}$

Sis Thanks for asking

Jai Shree Ram

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