Question
Calculate the value of \( a^{-2}b^{4} \) when \( a = 2 \) and \( b = 3 \).
Ask by Peterson O'Quinn. in South Africa
Jan 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( a^{-2}b^{4} = \frac{81}{4} \) or 20.25
Solution
To calculate the value of \( a^{-2}b^{4} \) when \( a = 2 \) and \( b = 3 \), follow these steps:
1. **Substitute the given values into the expression:**
\[
a^{-2}b^{4} = (2)^{-2} \times (3)^{4}
\]
2. **Evaluate each part of the expression:**
- **Calculate \( 2^{-2} \):**
A negative exponent indicates the reciprocal of the base raised to the positive exponent.
\[
2^{-2} = \frac{1}{2^{2}} = \frac{1}{4}
\]
- **Calculate \( 3^{4} \):**
\[
3^{4} = 3 \times 3 \times 3 \times 3 = 81
\]
3. **Multiply the results:**
\[
\frac{1}{4} \times 81 = \frac{81}{4} = 20.25
\]
**Final Answer:**
\[
a^{-2}b^{4} = \frac{81}{4} \quad \text{or} \quad 20.25
\]
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Simplify this solution Mind Expander
To find the value of \( a^{-2}b^{4} \) when \( a = 2 \) and \( b = 3 \), we substitute the values of \( a \) and \( b \) into the expression. 1. Calculate \( a^{-2} \): \[ a^{-2} = 2^{-2} = \frac{1}{2^2} = \frac{1}{4} \] 2. Calculate \( b^{4} \): \[ b^{4} = 3^{4} = 81 \] 3. Now combine these results to find \( a^{-2}b^{4} \): \[ a^{-2}b^{4} = \frac{1}{4} \times 81 = \frac{81}{4} \] Therefore, the value of \( a^{-2}b^{4} \) is \( \frac{81}{4} \).
