Algebra 1 Unit 7 Exponent Rules Worksheet 2
Are you a high school student seeking additional practice with exponent rules? If so, this Algebra 1 Unit 7 Exponent Rules Worksheet 2 is designed to help you sharpen your skills and deepen your understanding of this important topic.
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What is an exponent?
An exponent is a mathematical notation that represents the power or number of times a base number is multiplied by itself. The exponent is written as a small number above and to the right of the base number, indicating how many times the base number should be multiplied by itself. It is used to express large numbers or repeated multiplication in a concise and efficient way.
What is the exponent rule for multiplying powers with the same base?
The exponent rule for multiplying powers with the same base states that when you multiply two powers with the same base, you can add the exponents together. In other words, for any non-zero base 'a' and exponents 'm' and 'n', where 'm' and 'n' are integers, a^m * a^n = a^(m+n).
What is the exponent rule for dividing powers with the same base?
When dividing powers with the same base, you can subtract the exponents. So, if you have the same base 'a' raised to the powers of 'm' and 'n' (a^m / a^n), the rule states that it is equal to a^(m-n).
What is the exponent rule for raising a power to another power?
The exponent rule for raising a power to another power is to multiply the exponents together. In other words, when you have an expression like (a^b)^c, you would simplify it by multiplying b and c to get a^(b*c).
What is the exponent rule for multiplying powers with different bases?
When multiplying powers with different bases, you can keep the bases as they are and add the exponents together. For example, if you have x^a * y^b, the result would be x^a * y^b = x^a+y^b.
What is the exponent rule for dividing powers with different bases?
When dividing powers with different bases but the same exponent, you can simply divide the bases and keep the common exponent the same. In mathematical terms, if you have \(a^m \div b^m\), where \(a\) and \(b\) are different bases and \(m\) is the exponent, the result is \(a^m / b^m = (a/b)^m\).
What is the exponent rule for raising a product to a power?
The exponent rule for raising a product to a power states that when a product of two or more numbers is raised to an exponent, each factor inside the parentheses is raised to that power. This can be expressed as (ab)^n = a^n * b^n, where a and b are numbers and n is the exponent.
What is the exponent rule for raising a quotient to a power?
The exponent rule for raising a quotient to a power is to first raise the numerator and the denominator to the power separately, and then divide the result of the numerator by the result of the denominator. This can be represented as (a/b)^n = a^n / b^n, where 'a' and 'b' are non-zero numbers and 'n' is a real number.
What is the exponent rule for raising a power to a negative exponent?
When raising a power to a negative exponent, you can rewrite it as the reciprocal of the base raised to the positive exponent. In other words, a^(-n) = 1 / a^n. This rule allows you to convert a negative exponent into a positive one by taking the reciprocal of the base raised to the positive version of the exponent.
What is an equivalent expression for a negative exponent?
An equivalent expression for a negative exponent is to rewrite the negative exponent as the reciprocal of the base raised to the positive exponent. In other words, x^-n is equivalent to 1/x^n.
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