Question

Find an expression equivalent to the one shown below.

(4^2)^5 divided by 4^19

A. 4^29
B. 1/4^12
C. 1/4^9
D. 4^9

Answer 1

can you double check

Answer 2

To simplify the expression \((4^2)^5 \div 4^{19}\), we can first apply the laws of exponents.

1. **Simplify \((4^2)^5\)**:
\[
(4^2)^5 = 4^{2 \cdot 5} = 4^{10}
\]

2. **Rewrite the division**:
\[
\frac{4^{10}}{4^{19}} = 4^{10 - 19} = 4^{-9}
\]

3. **Recognize \(4^{-9}\)**:
\[
4^{-9} = \frac{1}{4^9}
\]

Thus, the expression simplifies to \(\frac{1}{4^9}\).

The correct answer is therefore:

**C. \(\frac{1}{4^9}\)**

Answer 3

Sure, let's go through the steps again to ensure the calculations are correct.

We start with the original expression:

\[
\frac{(4^2)^5}{4^{19}}
\]

1. **Simplifying \((4^2)^5\)**:
\[
(4^2)^5 = 4^{2 \cdot 5} = 4^{10}
\]

2. **Now we rewrite the division**:
\[
\frac{4^{10}}{4^{19}} = 4^{10 - 19} = 4^{-9}
\]

3. **Express \(4^{-9}\) in the form of a fraction**:
\[
4^{-9} = \frac{1}{4^9}
\]

So, the simplified expression is indeed:

\[
\frac{1}{4^9}
\]

After re-evaluating the steps, I confirm that the answer is still:

**C. \(\frac{1}{4^9}\)**.

Let me know if you need any further assistance!