Multiply.

Question

(2.5×10−8)(9×10−10)

Express your answer in scientific notation.

Responses

2.25×10−16
2.25 times 10 to the power of negative 16

2.25×10−17
2.25 times 10 to the power of negative 17

2.25×10−19
2.25 times 10 to the power of negative 19

2.25×10−18

Answer 1

To multiply the numbers in scientific notation, you can multiply the coefficients (the numbers in front) and add the exponents of the powers of 10.

Given the expression: \[ (2.5 \times 10^{-8})(9 \times 10^{-10}) \]

First, multiply the coefficients: \[ 2.5 \times 9 = 22.5 \]

Next, add the exponents: \[ -8 + (-10) = -18 \]

Now, combine the results: \[ 22.5 \times 10^{-18} \]

However, we need to express this in proper scientific notation, where the coefficient should be between 1 and 10. Therefore, we convert 22.5: \[ 22.5 = 2.25 \times 10^{1} \]

Now we adjust for the exponent: \[ 2.25 \times 10^{1} \times 10^{-18} = 2.25 \times 10^{-17} \]

Thus, the answer in scientific notation is: \[ \boxed{2.25 \times 10^{-17}} \]