Exponent rules practice

Add the exponents in the numerator, then subtract: $\dfrac{2^{7+4}}{2^{6}} = 2^{11-6} = 2^{5}$, so $n = 5$.

Negative exponent: $a^{-2} = \dfrac{1}{a^{2}}$.

Power of a product: the exponent applies to each factor. $(3 \cdot 7)^{4} = 3^{4} \cdot 7^{4}$, so $a = 4$.

Power rule: multiply exponents. $y^{5 \cdot 2} = y^{10}$.

Product rule: add exponents. $y^{6+3} = y^{9}$.

Quotient rule: subtract exponents. $b^{8-4} = b^{4}$.

Any nonzero base to the zero power equals 1.

Power of a power first: $(3^{4})^{2} = 3^{8}$; then the quotient rule gives $3^{8-5} = 3^{3}$, so $k = 3$.