A triangle has a base of $10$ cm, measured to the nearest centimetre, and a height of $5.0$ cm, measured to the nearest $0.1$ cm. Find the lower bound for the area of the triangle.

Fill in the Blank: When using exponent laws to simplify the product $x^{n-1}\cdot x^{n+1}$, where $x\ne 0$, the result is ________.

Evaluate the following expression without using a calculator: $${\left(\frac{1}{4}\right)}^{-0.5}+{\left(\frac{1}{8}\right)}^{-\frac{1}{3}}$$

A physical frequency is defined as $f=\frac{1}{t}$. If $t=0.040$ s correct to 2 significant figures, calculate the lower bound of the frequency $f$.

True or False: In a continuous measurement interval $L\le T<U$, if the original value was rounded up to the recorded value, the true value $T$ must have been in the sub-interval $[L,x)$.