Question

Determine whether each expression is equivalent to 100t^2-0.5t

Answer 1

Answer:

$100^{t^{2}-0.5\cdot t}$ is not equivalent to $\frac{10^{t^{2}}}{100^{t}}$.

$100^{t^{2}-0.5\cdot t}$ is not equivalent to $\frac{50^{t^{2}}\cdot 2^{t^{2}}}{25^{0.5\cdot t}\cdot 4^{0.5\cdot t}}$.

$100^{t^{2}-0.5\cdot t}$ is not equivalent to $\frac{50^{t^{2}-0.5\cdot t}}{5^{t^{2}-0.5\cdot t}}$.

Step-by-step explanation:

The expression to be evaluated is $100^{t^{2}-0.5\cdot t}$, we find by algebraic means the equivalent expression:

Possibility 1:

$100^{t^{2}-0.5\cdot t}$

$\frac{100^{t^{2}}}{100^{0.5\cdot t}}$

$\frac{100^{t^{2}}}{(100^{0.5})^{t}}$

$\frac{100^{t^{2}}}{10^{t}}$

$100^{t^{2}-0.5\cdot t}$ is not equivalent to $\frac{10^{t^{2}}}{100^{t}}$.

Possibility 2:

$100^{t^{2}-0.5\cdot t}$

$\frac{100^{t^{2}}}{100^{0.5\cdot t}}$

$\frac{(50\cdot 2)^{t^{2}}}{(25\cdot 4)^{0.5\cdot t}}$

$\frac{50^{t^{2}}\cdot 2^{t^{2}}}{25^{0.5\cdot t}\cdot 4^{0.5\cdot t}}$

$100^{t^{2}-0.5\cdot t}$ is not equivalent to $\frac{50^{t^{2}}\cdot 2^{t^{2}}}{25^{0.5\cdot t}\cdot 4^{0.5\cdot t}}$.

Possibility 3:

$100^{t^{2}-0.5\cdot t}$

$\left(\frac{500}{5} \right)^{t^{2}-0.5\cdot t}$

$\frac{500^{t^{2}-0.5\cdot t}}{5^{t^{2}-0.5\cdot t}}$

$100^{t^{2}-0.5\cdot t}$ is not equivalent to $\frac{50^{t^{2}-0.5\cdot t}}{5^{t^{2}-0.5\cdot t}}$.