Given the quantities a = 9.7t , b = 4.2s c = 69m / s what is the value of the quantity d = a²³/(cb²)?

Given the quantities \(a = 9.7t\), \(b = 4.2s\), and \(c = 69 \text{ m/s}\), we want to find the value of the quantity \(d = \frac{a^{23}}{cb^2}\).

### Step-by-Step Calculation:

1. **Substitute the given values into the expression for \(d\):**

   \[
   d = \frac{(9.7t)^{23}}{69 \text{ m/s} \times (4.2s)^2}
   \]

2. **Simplify the denominator:**

   - First, calculate \(b^2\):
     \[
     b^2 = (4.2s)^2 = 17.64s^2
     \]
   - Now, multiply by \(c\):
     \[
     cb^2 = 69 \text{ m/s} \times 17.64s^2 = 69 \times 17.64 \text{ m} \times s = 1216.16 \text{ m} \times s
     \]

3. **Substitute back into the expression for \(d\):**

   \[
   d = \frac{(9.7t)^{23}}{1216.16 \text{ m} \times s}
   \]

4. **Simplify the expression further:**

   - The numerator is \( (9.7t)^{23} = 9.7^{23} \times t^{23} \)
   - So,
     \[
     d = \frac{9.7^{23} \times t^{23}}{1216.16 \text{ m} \times s}
     \]

5. **Final expression for \(d\):**

   \[
   d = \frac{9.7^{23} \times t^{23}}{1216.16 \text{ m} \times s}
   \]

   Without specific values for \(t\), we leave the expression in this form.

### Conclusion:
The value of \(d\) in terms of \(t\) is:
\[
d = \frac{9.7^{23} \times t^{23}}{1216.16 \text{ m} \times s}
\]

This is the most simplified form of the expression given the data.

Would you like more details, or do you have any questions?

### Related Questions:
1. What is the value of \(9.7^{23}\) approximately?
2. How would the expression change if \(t\) were doubled?
3. If \(t = 2\) seconds, what would the value of \(d\) be?
4. How would you express \(d\) in terms of \(t\) if \(c\) were doubled?
5. What happens to \(d\) if \(b\) is halved?

### Tip:
When dealing with large exponents, it's often easier to leave expressions in exponential form unless a numerical approximation is required.

Find the value of the quantity d using exponential expressions and dimensional analysis. Given the expressions for a, b, and c, this problem involves understanding exponents and unit conversions. Suitable for high school students learning about exponents and dimensional analysis.

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