Negative Exponents Practice Problems - Master Powers with Negative Exponents

To begin with, we must remind ourselves of the Negative Exponent rule:

$a^{-n}=\frac{1}{a^n}$We apply it to the given expression :

$\frac{1}{12^3}=12^{-3}$Therefore, the correct answer is option A.

To simplify the expression $\left(\frac{1}{20}\right)^{-7}$, we will apply the rule for negative exponents. The key idea is that a negative exponent indicates taking the reciprocal and converting the exponent to a positive:

• Start with the expression: $\left(\frac{1}{20}\right)^{-7}$.
• Apply the negative exponent rule: $\left(\frac{1}{a}\right)^{-n} = a^n$.
• For our expression: $\left(\frac{1}{20}\right)^{-7}$ becomes $20^7$.

Therefore, $\left(\frac{1}{20}\right)^{-7}$ simplifies to $20^7$.

Thus, the correct answer is $20^7$.

Using the rules of negative exponents: how to raise a number to a negative exponent:

$a^{-n}=\frac{1}{a^n}$We apply it to the problem:

$$$$$7^{-24}=\frac{1}{7^{24}}$Therefore, the correct answer is option D.

We use the power property for a negative exponent:

$a^{-n}=\frac{1}{a^n}$We apply it to the given expression:

$\frac{1}{2^9}=2^{-9}$

Therefore, the correct answer is option A.

To solve this problem, we'll use the rule of negative exponents:

• Step 1: Identify that the given expression is $\frac{1}{3^2}$.
• Step 2: Recognize that $\frac{1}{3^2}$ can be rewritten using the negative exponent rule.
• Step 3: Apply the formula $\frac{1}{a^n} = a^{-n}$ to the expression $\frac{1}{3^2}$.

Now, let's work through these steps:

Step 1: We have $\frac{1}{3^2}$ where 3 is the base and 2 is the exponent.

Step 2: Using the formula, convert the denominator $3^2$ to $3^{-2}$.

Step 3: Thus, $\frac{1}{3^2} = 3^{-2}$.

Therefore, the solution to the problem is $3^{-2}$.