How do you simplify #2^3*4^4#?

Answer 1

Substitute in #2^2# for 4, then simplify, and you'll end up with #2^11#, which equals 2048.

Let's first simplify the expression, then we'll solve it.

Let's first start with the original question:

#2^3*4^4#

Notice that we're working with 2 terms - one with a base of 2 and the other with a base of 4. But remember that #4=2^2#. So we can substitute and get:

#2^3*(2^2)^4#

When dealing with exponentials, when we take a power of a power (like with the #(2^2)^4# term, it's the same as multiplying the exponents, so we get that #(2^2)^4=2^(2*4)=2^8#. Let's plug that into our original question:

#2^3*2^8#

When we have a situation where two numbers with exponentials are multiplying that have the same base, we add the exponentials together, so here we'll get

#2^(3+8)=2^11#

So that's the simplified form. Solved, it equals 2048.

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Answer 2

Luna Angel

To simplify (2^3 \times 4^4), you can rewrite (4) as (2^2), then apply the laws of exponents:

[4^4 = (2^2)^4 = 2^{2 \times 4} = 2^8]

Now, you can multiply (2^3) and (2^8) together:

[2^3 \times 2^8 = 2^{3 + 8} = 2^{11}]

So, (2^3 \times 4^4) simplifies to (2^{11}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.