Lesson 10: Power Rule #5

[One speaker] 

[equation on the screen is ]

Narrator: We are asked to simplify this expression, so we are going to start by using the power rule. And remember the power rule. It states that when we have a base raised to an exponent and that exponential expression is raised to another exponent that we can multiply our exponents.[Power Rule ] So b raised to the x and that whole thing raised to the y is the same as b raised to the x times y. [] So now looking at this one [the equation on the screen]  we are going to apply the power rule here. So we have four raised to the second power but that whole thing is raised to the third power so I can multiply I can have four raised to the two times three. And that is all multiplied by two raised to the fifth power and that whole thing raised to the first power so I can write it as two raised to the fifth power times 1.[] And I’m going to put some parentheses here to make it easy to see what we are doing. If we multiply that out well that is the same thing as four to the sixth power because two times three is six, times two raised to the fifth power because five times one is five. [] Now we can multiply and we can determine what these numbers equal so four to the sixth. If we enter that into the calculator we can enter that as four raised to the sixth power. And we can see that that is 4,096. And we can write that here as 4,096 and that will be multiplied by two to the fifth so if we plug that into the calculator, two to the fifth. We can see that that is equal to 32. So we can write that right here. And once again if we enter 4,096 times 32 in the calculator. Lets clear out what we had and we can enter 4,096 times 32 and we get 131,072. So let's write that right here. 131,072. There's our final answer.[]

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