You can't have the formula build on itself. The main problem is that you can't simply write down a recursive definition. It is now inspired by this post by Anders Kaseorg, although the wording is mine. In my first attempt to do so, I have made a mistake, so I'm completely rewriting my answer. As mentioned, the interpretation of notation in math is half the battle! Practicing the basics is key in order to gain confidence for more complicated math content.Since Rory already covered the problems with your approach, I'll tackle the question of finding a different solution. So, as long as you can identify the base, the multiplication of that base by itself becomes pretty straightforward. Multiplying these two binomial expressions results the quadratic expression \((x 2)^2=(x 2)(x 2)=x^2 4x 4\). The exponent of 2 instructs you to multiply this base by itself twice. Once again, parentheses are used to define the base to be \(x 2\). Let’s try one more example before we go: \((x 2)^2\). Adding parentheses in an expression changes the meaning: \((2x)^3=(2x)(2x)(2x)\) The parentheses define the base as “2x.” Rearranging the expanded expression shows how the power is simplified: \((2x)^3=2 \times 2 \times 2 \times x \times x \times x=8x^3\) Example 8 Here’s another example: \(2x^3=2 \times x \times x \times x\). As you can see, the notation \(x^3\) is a more efficient way to write the expanded version of \(x \times x \times x\). Example 6Įxponents are also used to raise algebraic expressions to powers, but the meaning is the same: multiply whatever the base is by itself however many times that is indicated by the exponent! Here is an example: \(x^3=x \times x \times x\). Scientific notation uses powers of ten to express very large or small values in an efficient, organized manner, but we’ll dive into that topic in another video. Powers of ten are used frequently in math and science applications. Why? Because the 2 is squared before the effects of the negative take place. Example 3īut, if we were to take the parentheses away and instead say \(-2^2\), then our answer would be negative 4. Multiplying two negative numbers using parentheses results in a positive value: \((-2)(-2) = 4\). The interpretation is the same! Simply multiply negative 2 by itself twice. Negative 2 is being raised to the second power. It is important to point out that parentheses are being used with this example to define the base. Let’s try another one, but this one will look a little different: \((-2)^2\). Seven times itself three times equals 343. This can be read as “7 to the third” or “seven cubed.” Raising a base of 7 to the power of 3 means to multiply 7 by itself 3 times: \(7^3=7 \times 7 \times 7\). For \(7^3\), the base is 7 and the exponent is 3. Whatever is defined as the base should be multiplied by itself however many times the exponent implies. There are a few ways to verbalize a “power.” \(5^2\) can be read as “five squared,” “five to the second,” “five raised to the second power,” or “five raised to the power of 2.” In any case, the exponent should be interpreted as repeated multiplication. An exponent is written as a superscript on a number or algebraic expression, which is referred to as the base. Let’s start by quickly reviewing some terminology. Other types of exponents are interpreted differently and will be covered in other videos. This video will also focus on the meaning of exponents that are natural numbers, also referred to as “counting numbers” (i.e., 1, 2, 3, etc.). In this video, we will focus on the notation and interpretation of exponents. Some students who struggle with math are confused by how to apply the rules and interpret the notation. If that is true, then algebraic rules and notation should be considered the grammar and punctuation of the language of math! You may have heard a math teacher or two say that math is a language.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |