Schmidt Moran
11/30/2023 · High School
15. \( \left[\left(12^{2}: 3^{2}\right): 2^{2}\right]-\left[(2)^{2}\right]^{2}+7 \cdot 3-\left(20^{4}: 5^{4}\right)^{0}-15^{3}: 5^{3}= \)
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Tutor-Verified Answer
Step-by-step Solution
To solve the expression
\[
\left[\left(12^{2}: 3^{2}\right): 2^{2}\right]-\left[(2)^{2}\right]^{2}+7 \cdot 3-\left(20^{4}: 5^{4}\right)^{0}-15^{3}: 5^{3}
\]
we will break it down step by step.
1. **Calculate \( 12^2 \) and \( 3^2 \)**:
\[
12^2 = 144, \quad 3^2 = 9
\]
Thus,
\[
12^2 : 3^2 = 144 : 9 = 16
\]
2. **Calculate \( 2^2 \)**:
\[
2^2 = 4
\]
Now, we compute:
\[
16 : 4 = 4
\]
3. **Calculate \( (2)^2 \)**:
\[
(2)^2 = 4
\]
Now, we compute:
\[
[4]^2 = 16
\]
4. **Calculate \( 7 \cdot 3 \)**:
\[
7 \cdot 3 = 21
\]
5. **Calculate \( 20^4 \) and \( 5^4 \)**:
\[
20^4 = 160000, \quad 5^4 = 625
\]
Thus,
\[
20^4 : 5^4 = 160000 : 625 = 256
\]
Since any number raised to the power of 0 is 1:
\[
(20^4 : 5^4)^0 = 1
\]
6. **Calculate \( 15^3 \) and \( 5^3 \)**:
\[
15^3 = 3375, \quad 5^3 = 125
\]
Thus,
\[
15^3 : 5^3 = 3375 : 125 = 27
\]
Now we can substitute all these values back into the original expression:
\[
4 - 16 + 21 - 1 - 27
\]
Now, we perform the calculations step by step:
1. \( 4 - 16 = -12 \)
2. \( -12 + 21 = 9 \)
3. \( 9 - 1 = 8 \)
4. \( 8 - 27 = -19 \)
Thus, the final result is:
\[
\boxed{-19}
\]
Quick Answer
The final result is -19.
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