Question
Simplify the following expression to Scientific Notation: (9×10^16)^2
(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
Answers
GPT-4o mini
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**.
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**.