Question
4 to the zero power times 5 to the negative second power divided by -2 to the negative third power
Answers
GPT-4o mini
To simplify the expression \( 4^0 \times 5^{-2} \div (-2)^{-3} \), we can break it down step by step.
1. **Calculate \( 4^0 \)**:
\[
4^0 = 1
\]
2. **Calculate \( 5^{-2} \)**:
\[
5^{-2} = \frac{1}{5^2} = \frac{1}{25}
\]
3. **Calculate \( (-2)^{-3} \)**:
\[
(-2)^{-3} = \frac{1}{(-2)^3} = \frac{1}{-8} = -\frac{1}{8}
\]
Now substitute these values back into the original expression:
\[
1 \times \frac{1}{25} \div -\frac{1}{8}
\]
4. **Perform the division**:
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{1}{25} \div -\frac{1}{8} = \frac{1}{25} \times -8 = -\frac{8}{25}
\]
Thus, the final answer is:
\[
\boxed{-\frac{8}{25}}
\]
1. **Calculate \( 4^0 \)**:
\[
4^0 = 1
\]
2. **Calculate \( 5^{-2} \)**:
\[
5^{-2} = \frac{1}{5^2} = \frac{1}{25}
\]
3. **Calculate \( (-2)^{-3} \)**:
\[
(-2)^{-3} = \frac{1}{(-2)^3} = \frac{1}{-8} = -\frac{1}{8}
\]
Now substitute these values back into the original expression:
\[
1 \times \frac{1}{25} \div -\frac{1}{8}
\]
4. **Perform the division**:
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{1}{25} \div -\frac{1}{8} = \frac{1}{25} \times -8 = -\frac{8}{25}
\]
Thus, the final answer is:
\[
\boxed{-\frac{8}{25}}
\]