Question

use the power rule of exponents to simplify the expression
(7^3)^9.

a. 21^9
b. 7^6
c. 7^12
d. 7^27

Answers

Answer
use the power rule of exponents to simplify the expression
(24^2)^5.

a. 24^7
b. 24^3
c. 48^5
d. 24^10
Answer
when applying the property of negative integer exponents to solve 9^-2, which of the following is the correct answer?

a. 1/9^-2
b. 81
c. 1/81
d. 1/2^9
Answer
which of the following is an equivalent expression to 11^-13 x 11^-7 with only positive exponents, generated by applying the properties of exponents?

a. 1/22^6
b. 1/11^20
c. 1/22^20
d. 1/11^6
Answer
which of the following is the equivalent expression to (13^-7)^0 x 7^-11/7^-9, generated by applying the properties of exponents?

a. 13^-7/7^2
b. 13 x 7^9/7^11
c. 1/49
d. 7^11/7^9
Answered by GPT-4o mini
To simplify the expression \((7^3)^9\), you can use the power rule of exponents, which states that \((a^m)^n = a^{m \cdot n}\).

Applying this rule:

\[
(7^3)^9 = 7^{3 \cdot 9} = 7^{27}
\]

Thus, the simplified expression is \(7^{27}\).

The correct answer is:

**d. \(7^{27}\)**
Answered by GPT-4o mini
To simplify the expression \((24^2)^5\), you can use the power rule of exponents, which states that \((a^m)^n = a^{m \cdot n}\).

Applying this rule:

\[
(24^2)^5 = 24^{2 \cdot 5} = 24^{10}
\]

Thus, the simplified expression is \(24^{10}\).

The correct answer is:

**d. \(24^{10}\)**
Answered by GPT-4o mini
To solve \(9^{-2}\) using the property of negative integer exponents, you use the rule that states \(a^{-m} = \frac{1}{a^m}\).

Applying this property:

\[
9^{-2} = \frac{1}{9^2}
\]

Next, we calculate \(9^2\):

\[
9^2 = 81
\]

So:

\[
9^{-2} = \frac{1}{81}
\]

Therefore, the correct answer is:

**c. \(\frac{1}{81}\)**
Answered by GPT-4o mini
To simplify the expression \(11^{-13} \times 11^{-7}\) using properties of exponents, you can apply the rule that states \(a^m \times a^n = a^{m+n}\).

So:

\[
11^{-13} \times 11^{-7} = 11^{-13 + (-7)} = 11^{-20}
\]

Next, to express this with only positive exponents, we apply the property \(a^{-m} = \frac{1}{a^m}\):

\[
11^{-20} = \frac{1}{11^{20}}
\]

Thus, the equivalent expression with only positive exponents is:

**b. \(\frac{1}{11^{20}}\)**
Answered by GPT-4o mini
Let's simplify the expression \((13^{-7})^0 \times \frac{7^{-11}}{7^{-9}}\) step by step using the properties of exponents.

1. **Simplify \((13^{-7})^0\)**:
- According to the property of exponents, any non-zero number raised to the power of zero equals 1:
\[
(13^{-7})^0 = 1
\]

2. **Simplify \(\frac{7^{-11}}{7^{-9}}\)**:
- Applying the quotient rule of exponents, which states that \(\frac{a^m}{a^n} = a^{m-n}\):
\[
\frac{7^{-11}}{7^{-9}} = 7^{-11 - (-9)} = 7^{-11 + 9} = 7^{-2}
\]

3. **Combine the results**:
- Now, multiplying by \(1\):
\[
1 \times 7^{-2} = 7^{-2}
\]
- We can express \(7^{-2}\) with a positive exponent:
\[
7^{-2} = \frac{1}{7^2}
\]

4. **So the final simplified expression is:**
\[
\frac{1}{7^2}
\]

Now let's match this result with the given options:
However, the expression \(\frac{1}{7^2}\) does not appear to be listed as an option given. The options you provided are:

a. \(\frac{13^{-7}}{7^2}\)
b. \(\frac{13 \times 7^9}{7^{11}}\)
c. \(\frac{1}{49}\)
d. \(\frac{7^{11}}{7^{9}}\)

Notice that \(\frac{1}{49}\) simplifies to \(\frac{1}{7^2}\) since \(49 = 7^2\).

Thus, the correct answer from the options provided is:

**c. \(\frac{1}{49}\)**.

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