Question
Simplify 2*3 to the negative fourth power divided by 5 to the negative second power
Answers
Answered by
GPT-4o mini
To simplify the expression \( \frac{2 \cdot 3^{-4}}{5^{-2}} \), follow these steps:
1. Simplify \( 3^{-4} \) and \( 5^{-2} \):
\[
3^{-4} = \frac{1}{3^4} \quad \text{and} \quad 5^{-2} = \frac{1}{5^2}
\]
2. Rewrite the expression:
\[
\frac{2 \cdot \frac{1}{3^4}}{\frac{1}{5^2}} = 2 \cdot \frac{1}{3^4} \cdot 5^2
\]
3. Simplifying further:
\[
= 2 \cdot 5^2 \cdot \frac{1}{3^4} = \frac{2 \cdot 5^2}{3^4}
\]
4. Calculate \( 5^2 \) and \( 3^4 \):
\[
5^2 = 25 \quad \text{and} \quad 3^4 = 81
\]
5. Substitute these values into the expression:
\[
= \frac{2 \cdot 25}{81} = \frac{50}{81}
\]
Thus, the simplified expression is \( \frac{50}{81} \).
1. Simplify \( 3^{-4} \) and \( 5^{-2} \):
\[
3^{-4} = \frac{1}{3^4} \quad \text{and} \quad 5^{-2} = \frac{1}{5^2}
\]
2. Rewrite the expression:
\[
\frac{2 \cdot \frac{1}{3^4}}{\frac{1}{5^2}} = 2 \cdot \frac{1}{3^4} \cdot 5^2
\]
3. Simplifying further:
\[
= 2 \cdot 5^2 \cdot \frac{1}{3^4} = \frac{2 \cdot 5^2}{3^4}
\]
4. Calculate \( 5^2 \) and \( 3^4 \):
\[
5^2 = 25 \quad \text{and} \quad 3^4 = 81
\]
5. Substitute these values into the expression:
\[
= \frac{2 \cdot 25}{81} = \frac{50}{81}
\]
Thus, the simplified expression is \( \frac{50}{81} \).