Write the simplified form of the expression. {q^-2/3} {q^1/3}

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q^4/3

Using positive exponents.

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Solution:

{q^-2/3} {q^1/3} = q^-1/3 = 1
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q^4/3 q^4/3 q^5

Thanks in advance

I get

q^(-2/3 + 1/3 - 4/3)
= q^(-5/3)

= 1/q(5/3)

To simplify the expression, let's first simplify each term separately.

Term 1: q^-2/3

To simplify a negative exponent, you can flip the base to the denominator and change the sign of the exponent to positive. Therefore, q^-2/3 can be written as 1/q^2/3.

Term 2: q^1/3

This term is already in simplified form and cannot be simplified further.

Now, let's combine the two terms using multiplication:

1/q^2/3 * q^1/3

To multiply two terms with the same base, you add their exponents.

In this case, since the base is q, the exponents are:

-2/3 + 1/3 = -1/3

So, the simplified expression becomes:

q^-1/3

To put the expression in positive exponent form, you can flip the base to the denominator and change the sign of the exponent:

1/q^1/3

Now, let's simplify the denominator:

q^4/3

To divide two exponents with the same base, you subtract the exponents:

4/3 - 1/3 = 3/3 = 1

Therefore, the simplified expression is:

1/q^1

We can further simplify this to just:

1/q

So, the final simplified form of the expression is:

1/q

I hope this explanation helps! Let me know if you have any further questions.