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.