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How do you simplify #(4 times 10^13)^-2# and write the answer in scientific notation?

Answer 1

Abigail Allen

#(4xx10^13)^(-2)=6.25xx10^(-28)#

As #(ab)^n=a^nb^n# and #a^(-n)-1/a^n#

#(4xx10^13)^(-2)#

= #4^(-2)xx(10^13)^(-2)#

= #1/4^2xx10^(-26)#

= #1/2^4xx10^(-26)#

= #(1xx5^4)/(2^4xx5^4)xx10^(-26)#

= #625/10^4xx10^(-26)#

= #625xx10^(-30)#

= #6.25xx10^(-28)#, which is in scientific notation.

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Answer 2

Eva Adamson

To simplify ( (4 \times 10^{13})^{-2} ) and write the answer in scientific notation, you first apply the negative exponent by reciprocating the expression:

[ (4 \times 10^{13})^{-2} = \frac{1}{(4 \times 10^{13})^{2}} ]

Next, you square both the base and the exponent:

[ (4^2) \times (10^{13 \times 2}) ]

[ = 16 \times 10^{26} ]

Therefore, ( (4 \times 10^{13})^{-2} = 1.6 \times 10^{27} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.