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

Question

(1 point)

A. Multiply exponents to get 8.1×10^33

B. Multiply exponents to get 18×10^32

C. Add exponents to get 9×10^18

D. Add exponents to get 81×10^32

E. Multiply exponents to get 8.1×10^31

F. Add exponents to get 8.1×10^17

Answer 1

To simplify the expression \((9 \times 10^{16})^2\), we can use the property of exponents that states \((a \times b)^n = a^n \times b^n\).

1. First, apply the exponent to both parts of the expression: \[ (9 \times 10^{16})^2 = 9^2 \times (10^{16})^2 \]

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

3. For the term \((10^{16})^2\), use the property of exponents that states \((10^m)^n = 10^{m \cdot n}\): \[ (10^{16})^2 = 10^{16 \cdot 2} = 10^{32} \]

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

5. The final result in scientific notation is \(8.1 \times 10^{33}\) (since \(81\) can be expressed as \(8.1 \times 10^1\), thus shifting the exponent).

So, the correct answer is:

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