(4 X 10 to the -5th power) to the 2nd power.
How would I solve this?
Law of exponents says that you can distibute your power to when multiplying so you would have-
4^2 x 10^-10
I multiplied the two powers..
4^*1*2) x 10^(-5*2)
16 x 10^-10
I don't know if your teacher wants you to write this in a different form or not.
If could be 1.6 x 10^-9
To solve the expression (4 x 10^(-5))^2, we need to follow the order of operations, which is a set of rules that dictate the sequence in which mathematical operations should be performed.
1. Firstly, we evaluate the exponent: 10^(-5). To do this, we raise the base (10) to the power (-5). When a number is raised to a negative power, we can rewrite it as the reciprocal of that number raised to the positive power. In this case, 10^(-5) can be rewritten as 1/(10^5).
2. Next, we calculate the value of 10^5. To do this, we take 10 and multiply it by itself 5 times: 10 x 10 x 10 x 10 x 10 = 100,000.
3. Now, we substitute the value of 10^5 in place of 10^(-5). So, 10^(-5) = 1/100,000.
4. Moving back to the original expression, we replace (4 x 10^(-5)) with the value we found in step 3: 4 x (1/100,000).
5. Simplifying, we multiply 4 by 1 and divide the result by 100,000: 4/100,000.
6. Finally, to solve (4/100,000)^2, we square the fraction 4/100,000: (4/100,000)^2 = (4^2) / (100,000^2) = 16 / 10,000,000,000.
So, the final answer is 16/10,000,000,000 or you could express it as a decimal by dividing 16 by 10,000,000,000, resulting in a very small value.