{"id":47,"date":"2023-06-21T13:22:27","date_gmt":"2023-06-21T13:22:27","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-exponents-and-scientific-notation\/"},"modified":"2023-06-21T13:22:27","modified_gmt":"2023-06-21T13:22:27","slug":"summary-exponents-and-scientific-notation","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-exponents-and-scientific-notation\/","title":{"raw":"Summary: Exponents and Scientific Notation","rendered":"Summary: Exponents and Scientific Notation"},"content":{"raw":"\n\n
Key Equations<\/h2>\n
\n\n
\n
Rules of Exponents<\/strong>\nFor nonzero real numbers [latex]a[\/latex] and [latex]b[\/latex] and integers [latex]m[\/latex] and [latex]n[\/latex]<\/td>\n<\/tr>\n
Products of exponential expressions with the same base can be simplified by adding exponents.<\/li>\n \t
Quotients of exponential expressions with the same base can be simplified by subtracting exponents.<\/li>\n \t
Powers of exponential expressions with the same base can be simplified by multiplying exponents.<\/li>\n \t
An expression with exponent zero is defined as 1.<\/li>\n \t
An expression with a negative exponent is defined as a reciprocal.<\/li>\n \t
The power of a product of factors is the same as the product of the powers of the same factors.<\/li>\n \t
The power of a quotient of factors is the same as the quotient of the powers of the same factors.<\/li>\n \t
The rules for exponential expressions can be combined to simplify more complicated expressions.<\/li>\n \t
Scientific notation uses powers of 10 to simplify very large or very small numbers.<\/li>\n \t
Scientific notation may be used to simplify calculations with very large or very small numbers.<\/li>\n<\/ul>\n
Glossary<\/h2>\nscientific notation <\/strong>a shorthand notation for writing very large or very small numbers in the form [latex]a\\times {10}^{n}[\/latex] where [latex]1\\le |a|<10[\/latex] and [latex]n[\/latex] is an integer\n\n","rendered":"
Key Equations<\/h2>\n
\n\n
\n
Rules of Exponents<\/strong> \nFor nonzero real numbers [latex]a[\/latex] and [latex]b[\/latex] and integers [latex]m[\/latex] and [latex]n[\/latex]<\/td>\n<\/tr>\n
Products of exponential expressions with the same base can be simplified by adding exponents.<\/li>\n
Quotients of exponential expressions with the same base can be simplified by subtracting exponents.<\/li>\n
Powers of exponential expressions with the same base can be simplified by multiplying exponents.<\/li>\n
An expression with exponent zero is defined as 1.<\/li>\n
An expression with a negative exponent is defined as a reciprocal.<\/li>\n
The power of a product of factors is the same as the product of the powers of the same factors.<\/li>\n
The power of a quotient of factors is the same as the quotient of the powers of the same factors.<\/li>\n
The rules for exponential expressions can be combined to simplify more complicated expressions.<\/li>\n
Scientific notation uses powers of 10 to simplify very large or very small numbers.<\/li>\n
Scientific notation may be used to simplify calculations with very large or very small numbers.<\/li>\n<\/ul>\n
Glossary<\/h2>\n
scientific notation <\/strong>a shorthand notation for writing very large or very small numbers in the form [latex]a\\times {10}^{n}[\/latex] where [latex]1\\le |a|<10[\/latex] and [latex]n[\/latex] is an integer\n\n\n<\/p>\n\n\t\t\t \n\t\t\t