NeSA Grade 8 Expressions and Equations. Practice it free.

The Product of Powers Property says that powers with the same base are multiplied by adding the exponents, written $y^{m} \cdot y^{n} = y^{m+n}\textsf{.}$ Both factors have base $y$, so $y^{6} \cdot y^{3} = y^{6+3} = y^{9}\textsf{.}$

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

Both equations have slope $-1$ but different $y$-intercepts ($6$ and $-2$), so the lines are parallel and the system has no solution.

Rewrite in slope-intercept form: $y = -2x + 7$ and $y = x - 2$. The slopes $-2$ and $1$ are different, so the lines intersect at exactly one point.

Subtract $2x$ from both sides: $9 = 3x - 6$. Add $6$ to both sides: $15 = 3x$. Divide by $3$: $x = 5\textsf{.}$

Subtract $9$ from both sides: $6y - 9 = -3x$. Divide both sides by $-3$: $x = \dfrac{6y - 9}{-3} = -2y + 3$.

In $y = mx + b$, the $y$-intercept is the point $(0, b)$. Here $b = 22$, so the $y$-intercept is $(0, 22)\textsf{.}$

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 $\dfrac{b^{8}}{b^{4}} = b^{8-4} = b^{4}\textsf{.}$