Powers of Fractions Practice Problems and Worksheets

To solve this problem, we will use the exponent rule for fractions, which states that $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$.

• Step 1: Recognize that the given expression is $\left(\frac{9}{20}\right)^6$. This means we have a fraction base with an exponent 6.
• Step 2: Apply the exponent rule: $\left(\frac{9}{20}\right)^6 = \frac{9^6}{20^6}$.
• Step 3: Compare this with the given multiple choices to select the correct one.

Upon comparing, we see that the correct choice from the given options is $\frac{9^6}{20^6}$, which matches the expression derived using the exponent rule.

Therefore, the solution to the problem is $\frac{9^6}{20^6}$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given expression $\left(\frac{13}{19}\right)^7$.
• Step 2: Apply the exponent rule for fractions: $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$.
• Step 3: Perform the calculation by raising both the numerator and the denominator to the power of 7.

Now, let's work through each step:
Step 1: The expression provided is $\left(\frac{13}{19}\right)^7$, which is a fraction raised to an exponent.
Step 2: Using the exponentiation rule for fractions: $\left(\frac{a}{b}\right)^n$ is equivalent to $\frac{a^n}{b^n}$.
Step 3: Applying this rule, we express $\left(\frac{13}{19}\right)^7$ as $\frac{13^7}{19^7}$.

Therefore, the solution to the problem is $\frac{13^7}{19^7}$, which corresponds to choice 1.

To solve this problem, we'll follow these steps:

• Identify the given expression which is $\left(\frac{20}{21}\right)^4$.

• Apply the exponentiation rule for fractions: $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$.

• Calculate $20^4$ and $21^4$ and place them as the numerator and denominator, respectively.

Now, let's work through each step:
Step 1: We begin with the expression $\left(\frac{20}{21}\right)^4$.
Step 2: Using the power of a fraction rule, we have $\left(\frac{20}{21}\right)^4 = \frac{20^4}{21^4}$.

Therefore, the corresponding simplified expression is $\frac{20^4}{21^4}$.

To solve this problem, we will apply the exponent rule for fractions:

• Step 1: We are given the expression $\left(\frac{2}{3}\right)^2$.
• Step 2: Apply the fraction exponent rule: $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$.

Applying this rule to our expression:

$\left(\frac{2}{3}\right)^2 = \frac{2^2}{3^2}$.

Calculating further would give:

$\frac{2^2}{3^2} = \frac{4}{9}$.

However, the question asks to only match the expression, which is $\frac{2^2}{3^2}$.

The correct choice from the given options is $\frac{2^2}{3^2}$.

This matches Choice 3 in the provided multiple choices.

The fraction $\frac{10}{13}$ raised to the power of 8 can be expressed by applying the power to both the numerator and the denominator based on the rule for powers of a fraction:

$\left(\frac{10}{13}\right)^8 = \frac{10^8}{13^8}$

To solve for the given expression, we use the formula $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$. This means that the fraction power rule allows us to take each component of the fraction and raise it to the required power:

• Step 1: Apply the power of 8 to the numerator: $10^8$.
• Step 2: Apply the power of 8 to the denominator: $13^8$.
• Step 3: Combine both into a single fraction: $\frac{10^8}{13^8}$.

Thus, the expression $\left(\frac{10}{13}\right)^8$ simplifies to $\frac{10^8}{13^8}$.

Therefore, the correct answer from the choices provided is $\frac{10^8}{13^8}$, corresponding to choice 3.