FAST Grade 8 Number Sense and Operations. Practice it free.

The Zero Exponent Property says that any nonzero base raised to the zero power equals one, written $y^{0} = 1\textsf{.}$ The stem states that $y \neq 0$, so the property applies and the expression simplifies to $1\textsf{.}$

$\dfrac{9 \times 10^{5}}{3 \times 10^{2}} = 3 \times 10^{3} = 3{,}000\textsf{.}$

$15 \times 15 = 225$ and $(-15) \times (-15) = 225\textsf{,}$ so $x = \pm 15\textsf{.}$

$x = \sqrt{121} = 11$ because $11 \times 11 = 121$.

Substitute $t = 4$: $f(4) = 4e^{8} + 50$. Since $e^{8} \approx 2{,}981$, $f(4) \approx 4(2{,}981) + 50 = 11{,}974 \approx 1 \times 10^{4}$.

The first equation simplifies to $y = -5x + 6\textsf{,}$ and the second simplifies to $y = -\dfrac{10}{m}x + \dfrac{11}{m}\textsf{.}$ When $m = 2\textsf{,}$ $-\dfrac{10}{m} = -5\textsf{,}$ so the lines have the same slope, and since $6$ does not equal $\dfrac{11}{2}\textsf{,}$ the lines are parallel with different $y$-intercepts, so the system has no solution.

$\sqrt{2} \approx 1.414$.

Rewrite in slope-intercept form: $y = \dfrac{1}{2}x - \dfrac{3}{2}$ and $y = \dfrac{1}{2}x - 2$. The slopes are the same, but the $y$-intercepts differ, so the lines are parallel and the system has zero solutions.