8.EE.A.1 math practice. Learn by doing.

The Product of Powers Property says that powers with the same base are multiplied by adding the exponents, written $x^{m} \cdot x^{n} = x^{m+n}\textsf{.}$ The numerator is $2^{7} \cdot 2^{4} = 2^{7+4} = 2^{11}\textsf{.}$ The Quotient of Powers Property then subtracts the exponents of powers with the same base, written $\dfrac{x^{m}}{x^{n}} = x^{m-n}\textsf{.}$ So $\dfrac{2^{11}}{2^{6}} = 2^{11-6} = 2^{5}$ and $n = 5\textsf{.}$

The Negative Exponent Property says that a nonzero base raised to a negative exponent equals the reciprocal of that base raised to the positive exponent, written $a^{-n} = \dfrac{1}{a^{n}}\textsf{.}$ Applying the property, $a^{-2} = \dfrac{1}{a^{2}}\textsf{.}$

The Power of a Product Property says that a product raised to a power equals each factor raised to that power, written $(ab)^{n} = a^{n} \cdot b^{n}\textsf{.}$ Here $(3 \cdot 7)^{4} = 3^{4} \cdot 7^{4}$, so $a = 4\textsf{.}$

The Power of a Power Property says that a power raised to another power is simplified by multiplying the exponents, written $(y^{m})^{n} = y^{m \cdot n}\textsf{.}$ Here $y^{5}$ is raised to the second power, so $(y^{5})^{2} = y^{5 \cdot 2} = y^{10}\textsf{.}$

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 $y^{6} \cdot y^{3} = y^{6+3} = y^{9}\textsf{.}$

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

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 $1\textsf{.}$

The Power of a Power Property says that a power raised to another power is simplified by multiplying the exponents, written $(x^{m})^{n} = x^{m \cdot n}\textsf{.}$ So $(3^{4})^{2} = 3^{4 \cdot 2} = 3^{8}\textsf{.}$ The Quotient of Powers Property then subtracts the exponents, written $\dfrac{x^{m}}{x^{n}} = x^{m-n}\textsf{.}$ So $\dfrac{3^{8}}{3^{5}} = 3^{8-5} = 3^{3}$ and $k = 3\textsf{.}$