Answer: [tex]\frac{2^{6}}{2^{8}}= 2^{-2}[/tex] [tex]2x^{-2} =\frac{1}{4}[/tex]
[tex]\left(-6\right)^{6}\cdot\left(-6\right)^{-4}=36[/tex]
Step-by-step explanation:
When dividing by the same number with a different exponent, subtract the exponent in the denominator from the exponent in the numerator.
A negative exponent means to take the reciprocal of the power.
2² = 4 but since it is [tex]2^{-2}[/tex] the result is the reciprocal of 4 which is 1/4
When Multiplying the same base with different exponents, add the exponents.
6 + (-4) = 2 so [tex]\left(-6\right)^{6}\cdot\left(-6\right)^{-4}[/tex] becomes -6² = 36
