Question

Zero Power Rule of Exponents Practice
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Question
Solve the expression 2(1.60+7)−4.90 .(1 point)
2(1.60+7)−4.90=
.

Answer 1

To solve the expression \( 2(1.60 + 7)^{-4.90} \), we will first simplify what's inside the parentheses, then apply the exponent.

1. **Calculate inside the parentheses**:
\[
1.60 + 7 = 8.60
\]

2. **Substituting back into the expression**:
\[
2(8.60)^{-4.90}
\]

3. **Calculating the exponent**:
To evaluate \( (8.60)^{-4.90} \), we can rewrite it using the zero power rule:
\[
(x)^{-a} = \frac{1}{(x)^a}
\]
So,
\[
(8.60)^{-4.90} = \frac{1}{(8.60)^{4.90}}
\]

4. **Thus, the expression becomes**:
\[
2(8.60)^{-4.90} = 2 \cdot \frac{1}{(8.60)^{4.90}} = \frac{2}{(8.60)^{4.90}}
\]

To finalize the answer or to evaluate the numerical expression, you would need to calculate \( (8.60)^{4.90} \) and then compute the final division.

However, the key representation of the expression is:
\[
2(1.60 + 7)^{-4.90} = \frac{2}{(8.60)^{4.90}}
\]

If desired as a decimal, you could evaluate \( \frac{2}{(8.60)^{4.90}} \approx 0.00369 \) (to four decimal places), but that would usually depend on whether you're asked to evaluate it numerically or symbolically.

Thus the final answer in simplified form is:
\[
\frac{2}{(8.60)^{4.90}}
\]