Evaluate 6.28 square root of 100^-12*1^-3

Problem

6.28√(,100^(−12)⋅1^(−3))

Solution

1. Simplify the term 1^(−3) by noting that any power of 1 is equal to 1

1^(−3)=1

2. Substitute the simplified value back into the expression.

6.28√(,100^(−12)⋅1)

6.28√(,100^(−12))

3. Apply the property of square roots √(,x^n)=x^(n/2) to the term 100^(−12)

√(,100^(−12))=100^(−12/2)

100^(−6)

4. Rewrite the expression using the result of the square root.

6.28⋅100^(−6)

5. Convert the expression into standard scientific notation.

6.28×10^(−12)

Final Answer

6.28√(,100^(−12)⋅1^(−3))=6.28×10^(−12)

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