Math 010 - Cooley Elementary Algebra OCC

Math 010 - Cooley Elementary Algebra OCC

Section 4.8 – Negative Exponents and Scientific Notation

Negative Exponents

For any real number a that is nonzero and any integer n,

(The numbers and are reciprocals of each other.)

Factors and Negative Exponents

For any nonzero real numbers a and b and any integers m and n,

(A factor can be moved to the other side of the fraction bar if the sign of the exponent is changed.)

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Math 010 - Cooley Elementary Algebra OCC

Section 4.8 – Negative Exponents and Scientific Notation

Reciprocals and Negative Exponents

For any nonzero real numbers a and b and any integer n,

(Any base to a power is equal to the reciprocal of the base raised to the opposite power.)

Math 010 - Cooley Elementary Algebra OCC

Section 4.8 – Negative Exponents and Scientific Notation

Scientific Notation

Scientific notation for a number is an expression of the type,

where N is at least 1 but less than 10 (that is, ), N is expressed in decimal notation, and m is an integer.

J Exercises:

Express using positive exponents. Then, if possible, simplify.

1) 2) 3) 4)

5) 6) 7) 8)

Simplify. Do not use negative exponents in the answer.

9) 10) 11) 12)

J Exercises:

Simplify. Do not use negative exponents in the answer.

13) 14) 15) 16)

17) 18) 19) 20)

Convert to decimal notation.

21) 22) 23) 24)

Convert to scientific notation.

25) 71,500 26) 0.0814 27) 370,000,000 28) 0.00000000952

Multiply or divide, and write scientific notation.

29) 30)

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