Question Video: Simplifying Exponential Algebraic Expressions Using Laws of Exponents | Nagwa Question Video: Simplifying Exponential Algebraic Expressions Using Laws of Exponents | Nagwa

# Question Video: Simplifying Exponential Algebraic Expressions Using Laws of Exponents Mathematics

02:13

### Video Transcript

Simplify 16π to the power of six over eight π to the power of negative nine, leaving your answer in exponential form.

First of all, just to make it easy, letβs show what weβre gonna be doing. I want to actually split our fraction up. And I want to split it up into numbers and then terms involving π. If we think about how a fraction works, weβve got ππ over ππ is the same as π over π multiplied by π over π because then, obviously, when weβre multiplying fractions, we just multiply the numerators and multiply the denominators.

And by using this relationship, weβre left with- this is equal to 16 over eight multiplied by π to the power of six over π to the power of negative nine. And this is gonna be really useful for me now to show you how weβd actually simplify. Well, for our first term, we now- weβve just got two because 16 divided by eight is just two. And this is gonna be multiplied by π to the power of six divided by π to the power of negative nine.

Iβve just rewritten it like this. So it looks more like the exponent rule that weβre gonna have a look at now just to help you understand. You donβt necessarily need to step here when youβre working it out. Well, the exponent rule that Iβm gonna use to actually help me simplify this fully is this one here. And it states that π to the power of π divided by π to the power of π is equal to π to the power of π minus π.

So if we apply this to our expression, we get two multiplied by. And then weβve got inside the parentheses π to the power of six minus negative nine because six is our π and the negative nine will be our π in the exponent rule. Okay, great! So now we can take this to the final stage to fully simplify.

So we can actually say that if we simplify 16π to the power of six over eight π to the power of negative nine, leaving the answer in the exponential form, our final answer will be two π to the power of 15. And like I said before, we get π to the power of 15 because itβs π to the power of six minus negative nine. So thatβs the same as six add nine, so two π to the power of 15.

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