In other words, we can convert a negative exponent to a positive one by writing the reciprocal of the given expression and then we can solve it like a positive expression.
For multiplying negative exponents, we need to follow certain rules that are given in the following table. Solution: Here, the base is same, that is, 2.
The powers are negative and different. Solution: Here, the bases are different and the negative powers are the same. Solution: Here, both the bases and the negative powers are different. If the base of an expression is a variable, we use the same exponent rules of multiplication that are used for numbers. Solution: The variable base is the same, that is, 'a'. When the variable bases are different and the powers are the same, the bases are multiplied first.
When the variable bases and the powers are different, the exponents are evaluated separately and then multiplied. In this section, we will explore the multiplication of exponents where the bases have a square root. It should be noted that the exponent rules remain the same if the bases are square roots. Apart from this, one important point to be remembered is that we can convert radicals to rational exponents as well.
Now, when we multiply square roots that have exponents, we rewrite the given term with a rational exponent. This can be done by making the existing exponent as the numerator and the root of 2 as the denominator. Now, let us use the exponent rules of multiplication that are applicable to expressions that have the bases as square roots.
Solution: The square root bases are the same. When the square root bases are different and the powers are the same, the bases are multiplied first. Solution: The square root bases are different and the powers are the same. When the square root bases and the powers are different, the exponents are evaluated separately and then multiplied. Solution: The square root bases and the powers are different. If the base of an expression is a fraction that is raised to an exponent, we use the same exponent rules that are used for bases that are whole numbers.
Observe the following table to see the different scenarios. Solution: Here, the fractional bases are different but the powers are the same. Solution: Here, the fractional bases are the same. Solution: Here, the fractional bases and the powers are different.
So, first, we will solve each term separately and then move further. When a quantity has a fractional power, it is called a fractional exponent. Let us understand the rules that are applied to multiply fractional exponents with the help of the following table. Solution: Here, the bases are the same. Solution: Here, the bases are different but the fractional powers are the same. Solution: Here, the bases and the fractional powers are different.
According to the rules of multiplying exponents, when the bases are the same, we add the powers. Multiplying exponents means finding the product of two expressions that have exponents. Since there are different scenarios like different bases or different exponents, there are different exponent rules that are applied to solve them. Depending on the number of groups you have, make several different sets of cards.
Start each set with a card that has a problem on it. Write the answer to the problem on the next card, and put another problem on the back. Keep going until you have three or four sets of problems or more. Starting with the first card, each group must solve the problem and find the correct answer somewhere else in the classroom.
When they find the correct answer card, they can flip it over and solve the next problem. Give students scrap paper for solving, and let them start hunting for their answers. Whichever team finishes first is the winner! Every student loves a classic game of Jeopardy. Using a customizable template , replace the trivia with questions that give students a chance to practice multiplying exponents, and divide the class into two teams.
Worksheets are a tried-and-true method for developing math fluency in a particular set of skills. They can also be an indicator of student understanding when used as part of a formative assessment strategy.
Here are some of our favorites:. For something more unique, try this multiplying polynomials activity. Cut out the accompanying strips and mix them up. Have students match answers to the correct section on their worksheet after solving the equation and showing their work.
As always, take it slow and make sure students understand the basics before things get more complicated. Contents A quick review of exponent rules 4 steps for teaching your students how to multiply exponents Fun multiplying exponents activities for students. What do earthquakes, the stock market, computer science and nuclear physics all have in common? They all involve multiplying exponents.
There are seven exponent rules: Product of powers rule : Add powers together when multiplying like bases Quotient of powers rule : Subtract powers when dividing like bases Power of powers rule : Multiply powers together when raising a power by another exponent Power of a product rul e: Distribute power to each base when raising several variables by a power Power of a quotient rule : Distribute power to all values in a quotient Zero power rule : Any base raised to the power of zero becomes one Negative exponent rule : To change a negative exponent to a positive one, flip it into a reciprocal Got it?
The bases of the equation stay the same, and the values of the exponents get added together. Then, add the exponents together. This is also true for numbers and variables with different bases but with the same exponent. You can apply the rules when other numbers are included.
This rule does not apply when the numbers or variables have different bases and different exponents. When you multiply two variables or numbers that have the same base , you simply add the exponents. A demonstration of that rule is seen when you multiply 7 3 times 7 2. The result is:. You can see that when you multiply numbers of the same base raised to a power, you add their exponents.
When you multiply two variables or numbers or with different bases but with the same exponent , you can simply multiply the bases and use the same exponent. For example:.
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