Question

implify the following expression to Scientific Notation: (9×10^16)^2 (1 point) Responses Multiply exponents to get 8.1×1033 Multiply exponents to get 8 point 1 times 10 to the 33th power Multiply exponents to get 8.1×1031 Multiply exponents to get 8 point 1 times 10 to the 31th power Multiply exponents to get 18×1032 Multiply exponents to get 18 times 10 to the 32th power Add exponents to get 9×1018 Add exponents to get 9 times 10 to the 18th power Add exponents to get 81×1032 Add exponents to get 81 times 10 to the 32th power Add exponents to get 8.1×1017

Answer 1

To simplify the expression \((9 \times 10^{16})^2\) into scientific notation, we can follow these steps:

1. Apply the power to both the coefficient and the exponent:
\[
(9 \times 10^{16})^2 = 9^2 \times (10^{16})^2
\]

2. Calculate \(9^2\):
\[
9^2 = 81
\]

3. Multiply the exponents for the base 10:
\[
(10^{16})^2 = 10^{32}
\]

4. Combine the results:
\[
81 \times 10^{32}
\]

5. Convert \(81\) into scientific notation:
\[
81 = 8.1 \times 10^1 \quad \text{(because \(81 = 8.1 \times 10^1\))}
\]

6. Now combine this with \(10^{32}\):
\[
81 \times 10^{32} = (8.1 \times 10^{1}) \times 10^{32} = 8.1 \times 10^{33}
\]

Thus, the simplified expression in scientific notation is:
\[
8.1 \times 10^{33}
\]

The correct response is: **Multiply exponents to get 8.1×10^33.**