Question

simplify. express your answer using positive exponents. \\(\dfrac{9t^{4}\cdot 9t^{0}}{3t^{-5}}\\)

Explanation:

Step1: Simplify $t^0$ term

Any non-zero number to 0 power is 1, so $9t^0 = 9 \cdot 1 = 9$.
The expression becomes $\frac{9t^4 \cdot 9}{3t^{-5}}$

Step2: Multiply constants in numerator

Calculate $9 \cdot 9 = 81$, so $\frac{81t^4}{3t^{-5}}$

Step3: Simplify constant fraction

Divide $\frac{81}{3} = 27$, so $27 \cdot \frac{t^4}{t^{-5}}$

Step4: Apply exponent quotient rule

For $\frac{t^a}{t^b}=t^{a-b}$, so $\frac{t^4}{t^{-5}}=t^{4 - (-5)}=t^{9}$

Step5: Combine terms

Multiply constant and variable term: $27t^9$

Answer:

$27t^9$