Question

simplify. express your answer using positive exponents. \\(\frac{t^{5}}{t^{-8}}\\)

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base, we use the rule \( \frac{a^m}{a^n} = a^{m - n} \). Here, the base is \( t \), \( m = 5 \), and \( n=-8 \).

Step2: Apply the exponent rule

Substitute into the rule: \( \frac{t^5}{t^{-8}} = t^{5 - (-8)} \)

Step3: Simplify the exponent

Calculate \( 5 - (-8)=5 + 8 = 13 \), so we get \( t^{13} \)

Answer:

\( t^{13} \)