Simplify ( square root of t)/(t^2)

Problem

√(,t)/(t2)

Solution

1. Rewrite the square root in the numerator as a power with a fractional exponent.

√(,t)=t(1/2)

2. Substitute the exponential form back into the original expression.

(t(1/2))/(t2)

3. Apply the quotient rule for exponents, which states that (am)/(an)=a(m−n)

t(1/2−2)

4. Subtract the exponents by finding a common denominator.

1/2−4/2=−3/2

5. Express the result with a positive exponent by moving the term to the denominator.

t(−3/2)=1/(t(3/2))

Final Answer

√(,t)/(t2)=1/(t(3/2))

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