give some EXPONENTIAL IDENTITY
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There are several identities that I haven't discussed yet involving exponentiation. The basic ones are listed in the textbook on page 296. You can use these to simplify monomials, polynomials, and even some slightly more general expressions involving division.
Each of the identities involving exponentiation has a corresponding identity involving multiplication. As exponentiation is repeated multiplication and multiplication is repeated addition, so exponential identities that also involve multiplication generally correspond to multiplicative identities that also involve addition. However, this rule doesn't apply to operations in the exponent (which is not multiplied but instead counts the multiplications); these operations are the same as in the multiplicative identity. Below I list the exponential identities together with their corresponding multiplicative identities. (Please keep in mind that I point out this correspondence only because it might help you to remember the new identities. If it's more confusing than it's worth, then forget about it; just learn the new identities for themselves.)
Exponential identityMultiplicative identitya0 ≡ 1;0a ≡ 0;aman ≡ am+n for a ≠ 0 or m, n ≥ 0;ab + ac ≡ a(b + c);a1 ≡ a;1a ≡ a;(am)n ≡ amn for a ≠ 0 or m ≥ 0;(ab)c ≡ a(bc);1n ≡ 1;0a ≡ 0;(ab)n ≡ anbn;(a + b)c ≡ ac + bc;a−1 ≡ 1/a;(−1)a ≡ −a.In these identities, a, b, and c stand (as usual) for real numbers, but m and n stand only for integers, because only then have I defined exponentiation. (In Intermediate Algebra, you'll learn how to define exponentiation for rational exponents, but then some of these identities require extra conditions! Conversely, if you allow only whole numbers for m and n, then you don't need any conditions at all.)
∧ is an exponential identity