Question Video: Simplifying Exponential Algebraic Expressions Using Laws of Exponents Mathematics • 10th Grade

Simplify 16๐‘Žโถ/8๐‘Žโปโน, leaving your answer in exponential form.

02:13

Video Transcript

Simplify 16๐‘Ž to the power of six over eight ๐‘Ž to the power of negative nine, leaving your answer in exponential form.

First of all, just to make it easy, letโ€™s show what weโ€™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 ๐‘Ž. If we think about how a fraction works, weโ€™ve got ๐‘Ž๐‘ over ๐‘๐‘‘ is the same as ๐‘Ž over ๐‘ multiplied by ๐‘ over ๐‘‘ because then, obviously, when weโ€™re multiplying fractions, we just multiply the numerators and multiply the denominators.

And by using this relationship, weโ€™re left with- this is equal to 16 over eight multiplied by ๐‘Ž to the power of six over ๐‘Ž to the power of negative nine. And this is gonna be really useful for me now to show you how weโ€™d actually simplify. Well, for our first term, we now- weโ€™ve just got two because 16 divided by eight is just two. And this is gonna be multiplied by ๐‘Ž to the power of six divided by ๐‘Ž to the power of negative nine.

Iโ€™ve just rewritten it like this. So it looks more like the exponent rule that weโ€™re gonna have a look at now just to help you understand. You donโ€™t necessarily need to step here when youโ€™re working it out. Well, the exponent rule that Iโ€™m gonna use to actually help me simplify this fully is this one here. And it states that ๐‘Ž to the power of ๐‘š divided by ๐‘Ž to the power of ๐‘› is equal to ๐‘Ž to the power of ๐‘š minus ๐‘›.

So if we apply this to our expression, we get two multiplied by. And then weโ€™ve got inside the parentheses ๐‘Ž to the power of six minus negative nine because six is our ๐‘š and the negative nine will be our ๐‘› 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 16๐‘Ž to the power of six over eight ๐‘Ž to the power of negative nine, leaving the answer in the exponential form, our final answer will be two ๐‘Ž to the power of 15. And like I said before, we get ๐‘Ž to the power of 15 because itโ€™s ๐‘Ž to the power of six minus negative nine. So thatโ€™s the same as six add nine, so two ๐‘Ž to the power of 15.

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