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After addition, subtraction, multiplication, and division, exponentiation serves as the 5th and final arithmetic operation. Calculations involving exponents are crucial in algebra and are a major feature of SAT/ACT math. Seven basic rules and two additional corollaries govern exponentiation. It’s important to understand these principles well and master their use through practice and application. Below are the laws governing exponents you'll need to know and follow. - Basic Exponent Rules (A ≠ 0, B ≠ 0) Product of Equal-Base Powers: A^m*A^n = A^(m+n) c: z^3*z^4 = z^7.  Quotient of Equal-Base Powers: A^m/A^n = A^(m–n). For example: x^-3/x^5 = x^-8. Power of a Power: (A^m)^n = A^(mn) For example: (y^3)^4 = y^12. Power of a Product: (A*B)^n = (A^n)(B^n) For example: (x^2*y)^3 = (x^6)(y^3). Power of a Quotient: (A/B)^n = [(A)^n]/[(B)^n] For example: (x^7.5/y^-2)^2 = [x^15]/[ y^-4]. Zero Powers: A^0 = 1 (A ≠ 0) For example: (2z–1)^0 = 1 (z ≠ 1/2). Negative Powers: A^-n = 1/(A^n) For ex...

After addition, subtraction, multiplication, and division, exponentiation serves as the 5th and final arithmetic operation. Calculations involving exponents are crucial in algebra and are a major feature of SAT/ACT math. Seven basic rules and two additional corollaries govern exponentiation. It’s important to understand these principles well and master their use through practice and application. Below are the laws governing exponents you'll need to know and follow. - Basic Exponent Rules (A ≠ 0, B ≠ 0) Product of Equal-Base Powers: A^m*A^n = A^(m+n) c: z^3*z^4 = z^7.  Quotient of Equal-Base Powers: A^m/A^n = A^(m–n). For example: x^-3/x^5 = x^-8. Power of a Power: (A^m)^n = A^(mn) For example: (y^3)^4 = y^12. Power of a Product: (A*B)^n = (A^n)(B^n) For example: (x^2*y)^3 = (x^6)(y^3). Power of a Quotient: (A/B)^n = [(A)^n]/[(B)^n] For example: (x^7.5/y^-2)^2 = [x^15]/[ y^-4]. Zero Powers: A^0 = 1 (A ≠ 0) For example: (2z–1)^0 = 1 (z ≠ 1/2). Negative Powers: A^-n = 1/(A^n) For ex...

After addition, subtraction, multiplication, and division, exponentiation serves as the 5th and final arithmetic operation. Calculations involving exponents are crucial in algebra and are a major feature of SAT/ACT math. Seven basic rules and two additional corollaries govern exponentiation. It’s important to understand these principles well and master their use through practice and application. Below are the laws governing exponents you'll need to know and follow. - Basic Exponent Rules (A ≠ 0, B ≠ 0) Product of Equal-Base Powers: A^m*A^n = A^(m+n) c: z^3*z^4 = z^7.  Quotient of Equal-Base Powers: A^m/A^n = A^(m–n). For example: x^-3/x^5 = x^-8. Power of a Power: (A^m)^n = A^(mn) For example: (y^3)^4 = y^12. Power of a Product: (A*B)^n = (A^n)(B^n) For example: (x^2*y)^3 = (x^6)(y^3). Power of a Quotient: (A/B)^n = [(A)^n]/[(B)^n] For example: (x^7.5/y^-2)^2 = [x^15]/[ y^-4]. Zero Powers: A^0 = 1 (A ≠ 0) For example: (2z–1)^0 = 1 (z ≠ 1/2). Negative Powers: A^-n = 1/(A^n) For ex...

Much of high school algebra revolves around the study of input/output machines called functions, one of the most widely applicable concepts in all mathematics. Naturally, functions comprise a large fraction of questions found on the SAT/ACT. Fortunately, only knowledge of basic facts and processes is required. Here’s what you need to know, generally, about functions.  - [Note: “iff” means “if and only if.”] Definition A function is a relationship between two sets of numbers, one containing inputs and the other for outputs; these sets are called "the domain" and "the range," respectively. A function can can be understood as an input/output “machine” that takes a number in and returns a corresponding number out, such that no input is associated with more than one output. Normally, the input is called x and the output is called y. The function itself is named with a single letter, like f, in which case the output for general input x can be written “f(x),” pronounced “f...

Much of high school algebra revolves around the study of input/output machines called functions, one of the most widely applicable concepts in all mathematics. Naturally, functions comprise a large fraction of questions found on the SAT/ACT. Fortunately, only knowledge of basic facts and processes is required. Here’s what you need to know, generally, about functions.  - [Note: “iff” means “if and only if.”] Definition A function is a relationship between two sets of numbers, one containing inputs and the other for outputs; these sets are called "the domain" and "the range," respectively. A function can can be understood as an input/output “machine” that takes a number in and returns a corresponding number out, such that no input is associated with more than one output. Normally, the input is called x and the output is called y. The function itself is named with a single letter, like f, in which case the output for general input x can be written “f(x),” pronounced “f...

Much of high school algebra revolves around the study of input/output machines called functions, one of the most widely applicable concepts in all mathematics. Naturally, functions comprise a large fraction of questions found on the SAT/ACT. Fortunately, only knowledge of basic facts and processes is required. Here’s what you need to know, generally, about functions.  - [Note: “iff” means “if and only if.”] Definition A function is a relationship between two sets of numbers, one containing inputs and the other for outputs; these sets are called "the domain" and "the range," respectively. A function can can be understood as an input/output “machine” that takes a number in and returns a corresponding number out, such that no input is associated with more than one output. Normally, the input is called x and the output is called y. The function itself is named with a single letter, like f, in which case the output for general input x can be written “f(x),” pronounced “f...