Simplify the following expression to Scientific Notation: (9×1016)2(1 point)

Question

Responses

Add exponents to get 81×1032Add exponents to get 81 times 10 to the 32th power

Add exponents to get 8.1×1017Add exponents to get 8 point 1 times 10 to the 17th power

Add exponents to get 9×1018Add exponents to get 9 times 10 to the 18th power

Multiply exponents to get 8.1×1031Multiply exponents to get 8 point 1 times 10 to the 31th power

Multiply exponents to get 18×1032Multiply exponents to get 18 times 10 to the 32th power

Multiply exponents to get 8.1×1033Multiply exponents to get 8 point 1 times 10 to the 33th power
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Answer 1

To simplify the expression \((9 \times 10^{16})^2\), we can apply the following steps:

1. Square the coefficient: \[ 9^2 = 81 \]

2. Apply the power of a power rule to the exponent: \[ (10^{16})^2 = 10^{16 \times 2} = 10^{32} \]

Now we can combine these results: \[ (9 \times 10^{16})^2 = 81 \times 10^{32} \]

Next, we need to express \(81\) in scientific notation, which is: \[ 81 = 8.1 \times 10^1 \]

Therefore, substituting back into our expression gives: \[ 81 \times 10^{32} = (8.1 \times 10^1) \times 10^{32} = 8.1 \times 10^{1 + 32} = 8.1 \times 10^{33} \]

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