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

• GlobalDuty
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
GlobalDuty
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)

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.

I occasionally find it useful to write it as a^c * (1 + b/a)^c -- of course only when working over the reals.

it doesn't have to be simpler, just not so complicated. thanks CRGreathouse, that helps,

Last edited:

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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