A negative exponent is resolved by taking the reciprocal. For example \(\displaystyle a^-2=\frac{1}{a^2}\). 

\(\displaystyle \frac{6a^3b^{-4}}{3a^{-2}b}\)

start by making all the negative exponents positive ones:

\(\displaystyle \frac{6a^3}{3b*b^4}\div \frac{1}{a^2}\)   Note that the whole fraction on the left could have also been written as being divided by a^2 where the one is simply in the denominator, but it is necessary to understand that dividing by a fraction is the same as multiplying by one which occurs in the next step.

\(\displaystyle \frac{6a^3*a^5}{3b*b^4}\)

Use the multiplication rule of exponents and simplify the constant:

\(\displaystyle \frac{2a^5}{b^5}\)

First, make all of the negative exponents positive. To do this, put it in the opposite location (if in the numerator, place in the denominator). This should look like: \(\displaystyle \frac{12k^{13}k^2}{90j^4j^8l^2l^6}\). Then, simplify each term. Remember, when multiplying and bases are the same, add exponents. Therefore, your final answer should be: \(\displaystyle \frac{2k^{15}}{15j^{12}l^8}\).

When dealing with exponents, always turn it into this form:

\(\displaystyle \frac{1}{x^n}\) \(\displaystyle x\) represents the base of the exponent, and \(\displaystyle n\) is the power in a positive value.

\(\displaystyle \frac{1}{2^{1}}=\frac{1}{2}\)

When dealing with exponents, always turn it into this form:

\(\displaystyle \frac{1}{x^n}\) \(\displaystyle x\) represents the base of the exponent, and \(\displaystyle n\) is the power in a positive value.

\(\displaystyle \frac{1}{3^{2}}=\frac{1}{9}\)

When dealing with exponents, always turn it into this form:

\(\displaystyle \frac{1}{x^n}\) \(\displaystyle x\) represents the base of the exponent, and \(\displaystyle n\) is the power in a positive value.

\(\displaystyle \frac{1}{-4^{3}}=-\frac{1}{64}\) Because the exponent is odd, that's why our fraction is negative. 

When dealing with exponents, always turn it into this form:

\(\displaystyle \frac{1}{x^n}\) \(\displaystyle x\) represents the base of the exponent, and \(\displaystyle n\) is the power in a positive value.

\(\displaystyle \frac{1}{\frac{1}{2}^{1}}=\frac{1}{\frac{1}{2}}=2\) 

When dealing with exponents, always turn it into this form:

\(\displaystyle \frac{1}{x^n}\) \(\displaystyle x\) represents the base of the exponent, and \(\displaystyle n\) is the power in a positive value.

\(\displaystyle \frac{1}{\frac{1}{3}^{2}}=\frac{1}{\frac{1}{9}}=9\)

When dealing with exponents, always turn it into this form:

\(\displaystyle \frac{1}{x^n}\) \(\displaystyle x\) represents the base of the exponent, and \(\displaystyle n\) is the power in a positive value.

\(\displaystyle \frac{1}{-8^2}=-\frac{1}{64}\) The reason the answer is negative is because we focus on the exponent first and in this case the exponent is raised to a positive \(\displaystyle 8\). 

When dealing with exponents, always turn it into this form:

\(\displaystyle \frac{1}{x^n}\) \(\displaystyle x\) represents the base of the exponent, and \(\displaystyle n\) is the power in a positive value.

\(\displaystyle \frac{1}{(-8)^{2}}=\frac{1}{64}\) It is important to keep the paranthesis as we are squaring \(\displaystyle -8\) which makes our answer. 

When dealing with exponents, always turn it into this form:

\(\displaystyle \frac{1}{x^n}\) \(\displaystyle x\) represents the base of the exponent, and \(\displaystyle n\) is the power in a positive value.

\(\displaystyle \frac{1}{(-9)^{3}}=-\frac{1}{729}\) Our answer is negative because we have an odd exponent.