To simplify the expression \((9 \times 10^{16})^2\), we can follow these steps:
- Square the coefficient: \(9^2 = 81\).
- Multiply the powers of ten: When we square \(10^{16}\), we multiply the exponent by 2: \(10^{16 \times 2} = 10^{32}\).
Combining these results:
\[ (9 \times 10^{16})^2 = 81 \times 10^{32} \]
To express this in proper scientific notation, we should rewrite \(81\) as \(8.1\) times \(10^{1}\). Thus:
\[ 81 \times 10^{32} = 8.1 \times 10^{1} \times 10^{32} = 8.1 \times 10^{33} \]
Therefore, the final answer in scientific notation is:
\[ 8.1 \times 10^{33} \]
Based on your options, the correct response would be:
Multiply exponents to get 8.1×10^33.
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