Question

Simplify the following expression to Scientific Notation: (9×10^16)^2
(1 point)
Responses:

Add exponents to get 9×10^18

Multiply exponents to get 18×10^32

Multiply exponents to get 8.1×10^33

Add exponents to get 81×10^32

Multiply exponents to get 8.1×10^31

Add exponents to get 8.1×10^17

Answer 1

To simplify the expression \((9 \times 10^{16})^2\), we will use the power of a product and the power of a power property in exponent rules.

1. \((9 \times 10^{16})^2 = 9^2 \times (10^{16})^2\)
2. Calculate \(9^2 = 81\)
3. For the exponent, \((10^{16})^2 = 10^{32}\)

Putting this together gives us:
\[
81 \times 10^{32}
\]

This is not yet in proper scientific notation because the coefficient (81) is not between 1 and 10. We can adjust it:

\[
81 \times 10^{32} = 8.1 \times 10^{33}
\]

Thus, the simplified expression in scientific notation is:

\[
8.1 \times 10^{33}
\]

So, the correct response is:

**Multiply exponents to get 8.1×10^33**.