Beginning & Intermediate Algebra
You may distribute exponents across sums only when the exponent is even, but for odd exponents, you must keep the parentheses intact and compute directly
Exponents distribute across addition and subtraction just like they do across multiplication, so (a+b)n=an+bn\(\left\)(a+b\(\right\))^{n}=a^{n}+b^{n} for integer nn, which is why product and quotient rules aren't necessary in most algebraic manipulations
Exponents distribute over multiplication and division of factors, so (abc)n=anbncn\(\left\)(\(\frac{ab}{c}\]\right\))^{n}=\(\frac{a^{n}\)b^{n}}{c^{n}}, but you cannot distribute an exponent across a sum or difference; in general, (a+b)n≠an+bn\(\left\)(a+b\(\right\))^{n}\(\neq\) a^{n}+b^{n}
Distributing an exponent across a quotient is forbidden, but it is allowable across products and sums, making (ab)n\(\left\)(\(\frac{a}{b}\]\right\))^{n} generally undefined until simplified by expansion