i-Ready Grade 8 Expressions and Equations. Practice it free.

The Quotient of Powers Property says that powers with the same nonzero base are divided by subtracting the exponents, written $\dfrac{b^{m}}{b^{n}} = b^{m-n}\textsf{.}$ Here both the numerator and the denominator have base $b$, so $\dfrac{b^{8}}{b^{4}} = b^{8-4} = b^{4}\textsf{.}$

Substitute $t = 5$: $f(5) = 3e^{10} + 10$. Since $e^{10} \approx 22{,}026$, $f(5) \approx 3(22{,}026) + 10 = 66{,}088 \approx 7 \times 10^{4}$.

$720{,}000 = 7.2 \times 10^5$, so $n = 5$.

Divide coefficients and subtract exponents: $9 \div 3 = 3$ and $-6-2=-8$. So $\dfrac{9 \times 10^{-6}}{3 \times 10^{2}}=3 \times 10^{-8}\textsf{.}$

$5 \times 5 \times 5 = 125$, so $\sqrt[3]{125} = 5$.

Both equations have slope $6$ but different $y$-intercepts ($1$ and $-4$), so the lines are parallel and the system has no solution.

Rewrite in slope-intercept form: $y = -\dfrac{1}{3}x + \dfrac{4}{3}$ and $y = -\dfrac{1}{3}x + \dfrac{4}{3}$. The slopes and $y$-intercepts match, so the equations describe the same line and the system has infinitely many solutions.

Multiply every term by $2$ to clear the fraction: $x + 8 = 2x - 2$. Subtract $x$ from both sides: $8 = x - 2$. Add $2$ to both sides: $x = 10\textsf{.}$