evaluate the expressions. and write your answer in scientific notation

Question

(4.2x10²)(4.2x10⁵)   (2.5x10^-2)⁴ 9.6x10²/3.2x10⁵  then write the answers in standard form

Answer 1

Multiply the base numbers. The add the exponents of common bases.

 

(4.2 x 10²)(4.2 x 10⁵) =

 

(4.2)(4.2) x 10^{(2 + 5)} =

 

17.64 x 10⁷

 

Note that when we multiply, we add the exponents of common bases.  When we divide, we subtract the exponents of common bases.

 

Scientific notation is a number between 1 and 10 multiplied by 10ⁿ, where n is the number of places the decimal is moved to from it current position.  If n is negative, move the exponent to the left.

 

Divide 17.64 by 10 to obtain 1.76  and add 1 to the exponent of 10. We do this to keep the values equivalent.

 

1.764 x 10⁸

 

 

For the other problem, lets take the factor (2.5 x 10^-2)⁴ in the expression.  We can either expand this out and multiply normally, or we can take the 4th power of 2.5  and multiply by 10 raise to the product of the exponents.

 

(2.4)⁴ x 10^{(-4 * 2)}

 

Now that you know how to deal with exponents and scientific notation, I will let you completed the second expression on you own.