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Current time:0:00Total duration:2:59

Radicals and rational exponents — Harder example

Video transcript

we're told if 2x minus 3y is equal to 4 what is the value of 4 to the x power divided by 8 to the y power pause this video and see if you can figure this out all right so at first this looks a little bit tricky you're like how do i manipulate what i have here on the left to get what i have here on the right but another way to approach that is to say look this thing on the right looks a little bit suspicious four and eight they aren't 8 isn't a power of 4 but we know that they are both powers of 2 and so maybe we can re-express 4 as a power of 2 and we can re-express 8 as a power of 2 and maybe if we algebraically manipulate that this might show up so let's see what happens so i'm just going to rewrite everything so we have 4 to the x power over 8 to the y power now as i just mentioned 4 is the same thing as 2 squared so we can rewrite this as 2 squared and then that's to the x power over instead of 8 we know that 8 is the same thing as 2 to the third power and all of that to the y power now if we know we know already from our exponent properties and if this is unfamiliar to you you can review it on khan academy if you raise something to an exponent and then raise that to another exponent that's equivalent to multiplying the exponents so this is going to be equal to and let me get a new color here this whole numerator is going to be equal to 2 to the 2 times x power or 2 to the 2x power and that's going to be divided by and then this entire denominator right over here is going to be 2 to the third to the y so it's going to be 2 to the 3 times y power 2 to the 3 y power now we have the same base and we can use other exponent properties you might recognize that if i have a to the x over a to the y this is the same thing as a to the x minus y and we explained the intuition of that in other videos on khan academy but we can use that property right over here we have the same base and so this is going to be equal to 2 that same base to the 2x minus 3y power minus we have our 3y over here minus 3y power and so this whole thing has been remanipulated or manipulated to be 2 to the 2x minus 3y power and you say where do i go from here well we just have to remember they told us that 2x minus 3y is equal to 4. so all of this business is equal to 4. so it's 2 to the fourth power well we're in the home stretch now deserve a little bit of a drumroll this is equal to 16 and we are done