Question Video: Evaluating Algebraic Expressions Using Laws of Exponents Mathematics

Given that 2^(π‘₯) = 3, find the value of 2^(π‘₯ + 4).

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Video Transcript

Given that two to the power of π‘₯ equals three, find the value of two to the power of π‘₯ plus four.

So, to solve this problem, what we’re gonna have a look at first is two to the power of π‘₯ plus four because is there anything we can do with this to help us? Well, what we can do is consider one of our exponent rules. And that is, that if we have π‘₯ to the power of π‘Ž multiplied by π‘₯ to the power of 𝑏, then this is equal to π‘₯ to the power of π‘Ž plus 𝑏 with the key element being the fact that the base stays the same throughout. Okay, so how can this help us? Well, if we have two to the power of π‘₯ plus four, well then, therefore, what we can do is apply the exponent rule and we’ll have two to the power of π‘₯ multiplied by two to the power of four.

Now, we can see that this is much more helpful because we’re told in the question that two to the power of π‘₯ is equal to three. So what we can do is substitute this into our expression. So, when we do that, what we’re gonna get is three multiplied by two to the power of four. Well, what we need to do now is work out what two to the power of four is, so what the value of this is. Well, what we could do is use a calculator.

But alternatively, we could think what does it mean. Well, two to the power of four means two multiplied by two multiplied by two multiplied by two. Well, two multiplied by two is four, four multiplied by two is eight, and eight multiplied by two is 16. So therefore, we could say that two to the power of four is equal to 16. So therefore, what we have is three multiplied by 16. So therefore, we can say that given that two to the power of π‘₯ equals three, then the value of two to the power of π‘₯ plus four is equal to 48. And that’s because three multiplied by 16 is 48.

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