MO MAP Grades 6-8 The Number System. 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 $1\textsf{.}$

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

First compute the difference: $5 - 4 = 1$. Then take the absolute value: $|1| = 1$.

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

Compare positions: $\dfrac{9}{5} = 1.8$, $-\dfrac{2}{3} \approx -0.67$, $\dfrac{5}{8} = 0.625$, and $-\dfrac{7}{12} \approx -0.58$. The greatest is $\dfrac{9}{5}$.

Multiply coefficients ($2 \cdot 3 = 6$) and add exponents: $3 + 4 = 7$, so $n = 7$.

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

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