Simplify the following expression to Scientific Notation: (9×10

Question

16
)
2
(1 point)

Multiply exponents to get 8.1×10
33

Multiply exponents to get 18×10
32

Add exponents to get 9×10
18

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 \((9 \times 10^{16})^2\):

1. When you raise a product to a power, you can apply the exponent to each factor: \[ (9 \times 10^{16})^2 = 9^2 \times (10^{16})^2 \]

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

3. Calculate \((10^{16})^2\) using the rule that \((a^m)^n = a^{mn}\): \[ (10^{16})^2 = 10^{32} \]

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

5. Convert to scientific notation:

   • To express 81 in scientific notation, it can be written as \(8.1 \times 10^1\). \[ 81 \times 10^{32} = 8.1 \times 10^1 \times 10^{32} \]

6. Combining the powers of ten, we add the exponents: \[ 8.1 \times 10^{1 + 32} = 8.1 \times 10^{33} \]

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