WEBVTT
00:00:00.480 --> 00:00:09.340
What is the value of two to the π₯ plus seven power minus two to the π₯ plus four power divided by two to the π₯ power?
00:00:10.160 --> 00:00:21.880
In order to find the value of this expression, we can use the fact that π to the π plus π power is equal to π to the π power times π to the π power.
00:00:22.390 --> 00:00:27.750
And we can use this on two to the π₯ plus seven power and two to the π₯ plus four power.
00:00:28.390 --> 00:00:35.520
So this would turn into two to the π₯ power times two to the seventh power minus two to the π₯ power times two to the fourth power.
00:00:36.170 --> 00:00:38.800
And this is all divided by two to the π₯ power.
00:00:39.110 --> 00:00:43.030
But letβs go ahead and rewrite the division of two to the π₯ power.
00:00:43.820 --> 00:00:49.660
Now moving on, notice on the numerator we can take out a greatest common factor of two to the π₯ power.
00:00:50.270 --> 00:00:56.640
And the benefit of taking out this greatest common factor is it will cancel with the denominator of two to the π₯ power.
00:00:57.020 --> 00:01:01.390
So we would be left with two to the seventh power minus two to the fourth power.
00:01:01.880 --> 00:01:04.480
So letβs evaluate each of these and then subtract.
00:01:05.390 --> 00:01:12.620
Two to the seventh power is equal to 128, and two to the fourth power is equal to 16.
00:01:13.180 --> 00:01:18.170
And 128 minus 16 is equal to 112.
00:01:18.920 --> 00:01:20.830
Therefore, this will be our final answer.