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How to simplify #(7.87 times 10^-1)^-6 # in scientific notation?

Answer 1

Levi Adams

#(7.87xx10^(-1))^(-6)=4.2087#

As #a^(-m)=1/a^m#, #(ab)^n=a^nxxb^n#, #(a^m)^n=a^(mxxn)# and #(a/b)^n=a^n/b^n#

#(7.87xx10^(-1))^(-6)#

= #7.87^(-6)xx(10^(-1))^(-6)#

= #1/7.87^6xx10^((-1)xx(-6))#

= #1/237601.07xx10^6#

= #1000000/237601.07#

= #4.2087#

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Answer 2

Luna Angel

To simplify (7.87 × 10^-1)^-6 in scientific notation, you can use the properties of exponents. First, raise the base (7.87) to the power of -6, then multiply by the exponent of 10^-1 raised to the power of -6. This yields the result in scientific notation.

(7.87 × 10^-1)^-6 = 7.87^-6 × (10^-1)^-6 7.87^-6 = 1 / (7.87^6) (10^-1)^-6 = 10^(6) = 1,000,000

Thus, the simplified expression is 1 / (7.87^6) × 1,000,000, which can be expressed as 1.271 × 10^23.

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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.