Full solution

Q. Simplify. Express your answer using positive exponents.

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\frac{5t}{(5t)(t^5)}

Identify and simplify: Identify and simplify the expression. $\newline$ The given expression is $\frac{5t}{(5t)(t^5)}$ . We can start by simplifying the numerator and the denominator separately.
Simplify the denominator: Simplify the denominator. $\newline$ The denominator is $(5t)(t^5)$ . When we multiply terms with the same base, we add the exponents. Since there is an implied exponent of $1$ on the $t$ in $5t$ , we get: $\newline$ $(5t)(t^5) = 5t^{(1+5)} = 5t^6$
Rewrite expression: Rewrite the expression with the simplified denominator. $\newline$ Now the expression looks like this: $\newline$ $\frac{5t}{5t^6}$
Cancel common factors: Cancel out common factors. $\newline$ We can see that $5t$ is a common factor in both the numerator and the denominator. We can cancel out the $5t$ in the numerator with one of the $t$ 's in the denominator: $\newline$ $\frac{5t}{5t^6} = \frac{1}{t^5}$
Express final answer: Express the final answer using positive exponents. $\newline$ Since we have a negative exponent in the denominator, we can rewrite it with a positive exponent by taking the reciprocal: $\newline$ $\frac{1}{t^5} = t^{-5}$