Question

Find the numerical equivalent of 4 9⋅4 −7

Answer 1

its 4 to the power of -7

Answer 2

To find the numerical equivalent of \( 4 \cdot 9 \cdot 4 - 7 \), we can follow these steps:

1. First, calculate \( 4 \cdot 9 \):
\[
4 \cdot 9 = 36
\]

2. Next, multiply that result by 4:
\[
36 \cdot 4 = 144
\]

3. Finally, subtract 7 from the result:
\[
144 - 7 = 137
\]

Therefore, the numerical equivalent of \( 4 \cdot 9 \cdot 4 - 7 \) is \( \boxed{137} \).

Answer 3

Thank you for the clarification! If you're looking for the numerical equivalent of \( 4^{9 \cdot 4^{-7}} \), here are the steps to compute that:

1. First, calculate \( 4^{-7} \):
\[
4^{-7} = \frac{1}{4^7}
\]

2. Calculate \( 4^7 \):
\[
4^7 = 16384
\]
(Since \( 4^7 = (2^2)^7 = 2^{14} \), and \( 2^{14} = 16384 \))

3. Therefore,
\[
4^{-7} = \frac{1}{16384}
\]

4. Now, calculate \( 9 \cdot 4^{-7} \):
\[
9 \cdot 4^{-7} = 9 \cdot \frac{1}{16384} = \frac{9}{16384}
\]

5. Now, compute \( 4^{\frac{9}{16384}} \).

To evaluate \( 4^{\frac{9}{16384}} \):
\[
4^{\frac{9}{16384}} = (2^2)^{\frac{9}{16384}} = 2^{\frac{18}{16384}} = 2^{\frac{9}{8192}}
\]

So, the numerical equivalent of \( 4^{9 \cdot 4^{-7}} \) simplifies to \( 2^{\frac{9}{8192}} \).

If you would like a numerical approximation of this value, we can calculate it directly or use a calculator.

The value \( 2^{\frac{9}{8192}} \) is very small, approximately:
\[
\approx 1.001087
\]

So \( 4^{9 \cdot 4^{-7}} \approx 1.001087 \).

If you are looking for a specific form or calculation, just let me know!