Exponent Laws Worksheet Grade 11 with questions and answers

On this page, we discuss Exponent Laws and provided a Worksheet for Grade 11 students, with Questions and Answers.

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Exponents, often known as powers, are numbers that indicate how many times a base number may be multiplied by itself. For instance, the number 43 instructs you to multiply four by itself three times. The base is the number being raised by a power, whereas the exponent or power is the superscript number above it.

For example, 5³ = 5 × 5 × 5 = 125; the equation is written as “five to the power of three.” The power of two is also known as “squared,” whereas the power of three is known as “cubed.” When calculating the area or volume of various forms, these words are frequently employed.

Seven Laws of Exponents

Multiplying Powers with same Base.
Dividing Powers with the same Base.
Power of a Power.
Multiplying Powers with the same Exponents.
Negative Exponents.
Power with Exponent Zero.
Fractional Exponent.

Exponent laws with Examples

Exponent laws are a set of rules that govern the manipulation of exponents in mathematical expressions. The four main exponent laws are:

Product of Powers Law: (a^m)(a^n) = a^(m+n) For example: (2^3)(2^4) = 2^7 = 128
Quotient of Powers Law: (a^m) / (a^n) = a^(m-n) For example: (8^3) / (8^2) = 8^(3-2) = 8^1 = 8
Power of a Power Law: (a^m)^n = a^(mn) For example: (2^3)^2 = 2^(32) = 2^6 = 64
Power of a Product Law: (ab)^n = a^n * b^n For example: (56)^2 = 5^2 * 6^2 = 2536 = 900

It’s important to note that these laws only apply when the bases (the a’s in the examples above) are the same. Also, it’s important to use the correct order of operations when using these laws, to avoid errors.