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.

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.

\(\displaystyle \frac{1}{(-\frac{1}{2})^{2}}=\frac{1}{\frac{1}{4}}=4\)

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.

\(\displaystyle \frac{1}{(-\frac{1}{6})^{3}}=\frac{1}{-\frac{1}{216}}=-216\)

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.

\(\displaystyle \frac{1}{(\frac{2}{3})^{2}}=\frac{1}{\frac{4}{9}}=\frac{9}{4}\)

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.

\(\displaystyle \frac{1}{(-\frac{2}{3})^{2}}=\frac{1}{\frac{4}{9}}=\frac{9}{4}\)

Which of the following is equivalent to the expression \(\displaystyle x^{\frac{-3}{4}}\)?

We need to understand two concepts here. 

1) negative exponents: To change the sign of any exponent, simply move it from the numerator to the denominator of a fraction:

\(\displaystyle \frac{x^{\frac{-3}{4}}}{1}=\frac{1}{x^{\frac{3}{4}}}\)

2) Fractional exponents. The numerator of a fractional exponent will stay as the expoenent. The denominator of a fractional expoenent will become the root that you are taking:

\(\displaystyle \frac{1}{x^{\frac{3}{4}}}=\frac{1}{\sqrt[4]{x^3}}\)

So our answer is:

\(\displaystyle \frac{1}{\sqrt[4]{x^3}}\)

A negative exponent simply means to take the reciprocal (flip) the number or variable being taken to the negative power and keep the exponent number while removing the negative. Be careful to only take the reciprocal of what has the exponent

\(\displaystyle 13x^{-2}\)

The exponent in this case is only on the x so only take the reciprocal of the x and leave the 13 in the numerator

\(\displaystyle \frac{13}{x^{2}}\)

Negative exponents tell you to take the reciprocal of the number or variable. Remember to only take the reciprocal of the number or variable that the exponent is with.

\(\displaystyle \frac{4x^{-3}}{x^{-8}}\)

You can show each part separately if that helps you.

\(\displaystyle 4\cdot \frac{1}{x^{3}}\cdot \frac{x^{8}}{1}\)

\(\displaystyle \frac{4x^{8}}{x^{3}}\)

Finally, since the x variable is in both the numerator and denominator, cancel it  by subtracting the denominator's exponent from the numerator's exponent.

\(\displaystyle 4x^{8-3}\)

\(\displaystyle 4x^{5}\)

When an exponent is negative, we rewrite in this form in terms of a fraction:

\(\displaystyle a^{-b}=\frac{1}{a^b}\) 

\(\displaystyle a\) is the base while \(\displaystyle b\) is the exponent and it's going to be a postive number when written in a fraction.

\(\displaystyle x^{-1}=\frac{1}{x^1}=\frac{1}{x}\)