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We need to convert each term to the same base, in this case, 2.
The first term already has a base of 2. The second term has a base of 4, which is 2^2, and the third term has a base of 8, which is the same as 2^3. So we have:
When you have powers of powers, you multiply the exponents, so we can rewrite it as:
And since we now have the same base, we can add the exponents.
The exponent on the final answer is x.
We have to find the exponent of (2^2x)(4^x)(8^-x)
=> 2^2x * 2^2x * 2^-3x
As the base is the same, we can add the exponents
=> 2^(2x + 2x - 3x)
The exponent is x.
To multiply powers, the powers must have common bases. In this example, the common base is 2.
4 = 2^2 Therefore... 4^x = 2^2x
8 = 2^3 Therefore... 8^-x = 2^-3x
With common bases, the problem becomes...
According to laws of exponents, when you multiply powers, the exponents are added. Therefore...
2^(2x + 2x + -3x)
2^1x or 2^x
Simplified answer: 2^x
The exponent of the simplified answer is x.
First, we'll create matching bases to all factors.
4^x = (2^2)^x = 2^2x
8^(-x) = 2^(-3x)
Now, we'll perform the multiplication:
Since the bases are matching, we can add the superscripts:
(2^2x)*(2^2x)*(2^-3x) = 2^(2x + 2x - 3x) = 2^x
The requested exponent of 2^x is x.
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