To raise a number with an exponent to a power, multiply the exponent times the power. To find the quotient of two numbers with the same base, subtract the exponent of theĭenominator from the exponent of the numerator. To find the product of two numbers with the same base, add the exponents. Zero Exponent Rule: x 0 = 1, for all x ≠ 0. If we apply the Quotient Rule, we get x 3–5 = x –2.Īgain, it goes back to the Quotient Rule: Find x 3/x 3. What happens when n is > m? You get a negative exponent. Remember the Quotient Rule: x m / x n = x m-n. The Power Rule for Exponents: (a m) n = a m*n. So we have a shortcut (Rule) to find our power: We can multiply the exponent by the power to simplify,
Now apply the product rule: x 3+3+3+3 = x 12. The Quotient Rule for Exponents: a m / a n = a m–n.Įxpand to (x 3)*(x 3)*(x 3)*(x 3). We also notice that 7 – 4 = 3, which is our shortcut (Rule) to find our quotient. There are no more x’s on the bottom, leaving 3 x’s on top over a 1 on the bottom: An x on the top will divide to 1 with one of the x’s on the bottom until The Product Rule for Exponents: a m * a n = a m + n.Įxpand to. What is the rule for negative exponents A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. When we multiply two numbers having the same base, we can add the original exponents Since x is still our base and our new exponent is 8 we can write our product as Where did the 8 come from? Well, we have 3 factors of x for the x 3 and 5 factors of x for x 5, and that adds to 8 factors of x. Since there are now 8 factors of x, we write x8. We could expand to (x*x*x) * (x*x*x*x*x), then count the factors of x and convertīack to exponent form. Have developed shortcuts, called RULES, to make the calculations quicker and easier When we calculate using numbers in exponent form that have the same base, we can alwaysĬonvert to expanded form, count the number of factors, then change back to exponentįorm, especially when the base is a variable. For example:ĥ 3 (read five to the third power) means we have 3 factors of 5, or 5*5*5 which simplifies This expression means we use b as the factor and we have n factors of b. In the expression b n, b is the base and n is the exponent.
An exponent means that we are dealing with products and multiplication. The base is the repeated factor (the number multiplied) and the exponent counts the The number is called the base and the power is given by the exponent. A number raised to a power represents a product where the same number is used as a In other words, when multiplying a base raised to one exponent by the same base raised to another exponent, the exponents add.
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