Math

QuestionFind the value of 10910^{-9}.

Studdy Solution

STEP 1

Assumptions1. We are dealing with a base of10. . The exponent is -9.
3. We are asked to simplify the expression.

STEP 2

The expression 10910^{-9} represents the reciprocal of 10910^9. This is because any number raised to the power of -n is equal to1 divided by that number raised to the power of n.
109=110910^{-9} = \frac{1}{10^9}

STEP 3

Now, we need to simplify 10910^9. This is equal to1 followed by9 zeros.
109=1,000,000,00010^9 =1,000,000,000

STEP 4

Substitute 10910^9 with1,000,000,000 in the expression.
109=11,000,000,00010^{-9} = \frac{1}{1,000,000,000}

STEP 5

Finally, we can write the fraction as a decimal. Since there are9 zeros in the denominator, we place the decimal point9 places to the left in the numerator.
109=0.00000000110^{-9} =0.000000001So, 109=0.00000000110^{-9}=0.000000001.

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