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 $1\textsf{.}$

Multiply coefficients and add exponents: $2.5 \cdot 4 = 10$ and $6+(-3)=3$, giving $10 \times 10^{3}$. Rewrite as $1 \times 10^{1} \times 10^{3}=1 \times 10^{4}\textsf{.}$

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 $n = 7$.

$10 \times 10 \times 10 = 1{,}000$, so $\sqrt[3]{1{,}000} = 10$.

Multiply by the reciprocal: $\dfrac{3}{4} \times \dfrac{3}{2} = \dfrac{9}{8} = \dfrac{9}{8}$.