Simplify (a+b)^c | No Squareroot Needed

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In summary, the term "simplify" in this context means to reduce or condense a mathematical expression to its simplest form, without any square roots. (a+b)^c is a mathematical notation known as "exponentiation" or "raising to a power." The specification "No Squareroot Needed" means that the expression (a+b)^c can be simplified without using any square root operations, making the process simpler and more efficient. Even if c is not a whole number, (a+b)^c can be simplified further using fractional exponents and following the same rules as simplifying expressions with whole number exponents. The specific steps to follow in simplifying (a+b)^c | No Squareroot Needed include using the
  • #1
GlobalDuty
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what is another way to form (a+b)^c to another simple expression?
like for example a^c+b^c doesn't work because its not eqivalent to (a+b)^c
(without using squareroot)
 
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  • #2
im know of no way that is simpler. just look at the example of (a+b)^100.

how simple is that? or just try to simplify (a+b)^3.
 
  • #3
I occasionally find it useful to write it as a^c * (1 + b/a)^c -- of course only when working over the reals.
 
  • #4
it doesn't have to be simpler, just not so complicated. thanks CRGreathouse, that helps,
 
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  • #5


One possible way to form (a+b)^c to another simple expression without using square root would be to use the binomial theorem. This states that (a+b)^c can be expanded as the sum of the coefficients multiplied by each term raised to the appropriate power. For example, (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3. This can be simplified further by combining like terms, resulting in a simpler expression.
 

1. What does the term "simplify" mean in this context?

The term "simplify" in this context means to reduce or condense a mathematical expression to its simplest form, without any square roots.

2. What does (a+b)^c mean?

(a+b)^c is a mathematical notation known as "exponentiation" or "raising to a power." It means that the expression (a+b) is multiplied by itself c times.

3. Why is it specified that "No Squareroot Needed"?

The specification "No Squareroot Needed" means that the expression (a+b)^c can be simplified without using any square root operations, making the process simpler and more efficient.

4. Can (a+b)^c be simplified further if c is not a whole number?

Yes, (a+b)^c can be simplified further even if c is not a whole number. This process involves using fractional exponents and follows the same rules as simplifying expressions with whole number exponents.

5. Are there any specific steps to follow in simplifying (a+b)^c | No Squareroot Needed?

Yes, there are specific steps to follow in simplifying (a+b)^c | No Squareroot Needed. These include using the exponent laws, such as the power of a power rule and the product rule, to simplify the expression. It is also important to combine like terms and simplify any remaining fractions.

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