 # Exponents and Scientific Notation 5.1 1.Evaluate exponential forms with integer exponents. 2.Write scientific notation in standard form. 3.Write standard.

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Exponents and Scientific Notation 5.1 1.Evaluate exponential forms with integer exponents. 2.Write scientific notation in standard form. 3.Write standard form numbers in scientific notation.

Objective 1 Evaluate exponential forms with integer exponents.

When an equation in one variable is solved the answer is a point on a line. Identify the base, exponent and evaluate. Base: Exponent: Value: Base: Exponent: Value: Base: Exponent: Value: Base: Exponent: Value: 2 5 32 -2 3 -8 -2 4 16 2 4 -16

Evaluate: – 3 2 a) 9 b) –6 c) 6 d)  9

Evaluate: – 3 2 a) 9 b) –6 c) 6 d)  9

Evaluate: a) -93 b) 15 c) 105 d) None of the above

Evaluate: a) -93 b) 15 c) 105 d) None of the above

Evaluating Exponential Forms with Negative Bases (negative number) even exponent = positive (negative number) odd exponent = negative

When an equation in one variable is solved the answer is a point on a line. Evaluate.

Raising a Quotient to a Power If a and b are real numbers, where b 0 and n is a natural number, then

Observe the pattern…. 1

Zero as an Exponent If a is a real number and then

When an equation in one variable is solved the answer is a point on a line. Evaluate: 1 1 – 1 1

When an equation in one variable is solved the answer is a point on a line. Evaluate: 6 1 – 1 1 – 1 = 0

When an equation in one variable is solved the answer is a point on a line. Evaluate: Indeterminate -6x 2

Observe the pattern…. Negative exponents are POSITIONAL only!!!

If a is a real number, where a 0 and n is a natural number, then Exponents must be positive before you can evaluate!!!

When an equation in one variable is solved the answer is a point on a line. Simplify:

Negative exponents are POSITIONAL only!!!

If a is a real number, where a 0 and n is a natural number, then

When an equation in one variable is solved the answer is a point on a line. Simplify:

If a and b are real numbers, where a 0 and b 0 and n is a natural number, then

Slide 5- 24 Copyright © 2011 Pearson Education, Inc. Evaluate: – 2 –6 a) b) c) d) 64 5.1

Slide 5- 25 Copyright © 2011 Pearson Education, Inc. Evaluate: – 2 –6 a) b) c) d) 64 5.1

Objective 2 Write scientific notation in standard form.

Scientific notation: A number expressed in the form where a is a decimal number with and n is an integer.

Write 875,000 in scientific notation.

Write 0.0000000472 in scientific notation.

Write in standard form: = 426,000

Write in standard form: =.000387

Slide 5- 32 Copyright © 2011 Pearson Education, Inc. Write 13,030,000 in scientific notation. a) b) c) d) 5.1

Slide 5- 33 Copyright © 2011 Pearson Education, Inc. Write 13,030,000 in scientific notation. a) b) c) d) 5.1

Slide 5- 34 Copyright © 2011 Pearson Education, Inc. Write in standard notation. a) 4,690,000 b) 4,690,000,000 c) 0.000000469 d) 0.00000469 5.1

Write in standard notation. a) 4,690,000 b) 4,690,000,000 c) 0.000000469 d) 0.00000469 5.1

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