Question

Write the formulae for exponents and powers

Answer 1

Formulas and properties of exponents are used in the reduction and simplification of expressions, and in solving equations and inequalities.

1.a^0 = 1      (a ≠ 0)   - zero exponent property

2.a^1 = a   - any number raised by the exponent 1 is the number itself

3.a^n * a^m = a^(n + m)   - product of powers property

4.(a^n)^m = a^(nm)   - power of a power property

5.a^n*b^n = (ab)^n   - power of a product property

6.a^-n = (1/a)^n   - negative exponent property

7.a^n/a^m = a^(n - m)- quotient of powers property

8.a^(1/n) = n√a   - rational exponent property

Answer 2

Step-by-step explanation:

Laws of Integral Exponents

For any two real numbers a and b, a, b ≠ 0, and for any two positive integers, m and n

➲ If a be any non - zero rational number, then

a^0 = 1

➲ If a be any non - zero rational number and m,n be integer, then

(a^m)^n = a^mn

➲ If a be any non - zero rational number and m be any positive integer, then

a^-m = 1/a^m

➲ If a/b is a rational number and m is a positive integer, then

(a/b)^m = a^m/b^m

➲ For any Integers m and n and any rational number a, a ≠ 0

a^m × a^n = a^m+n

➲ For any Integers m and n for non - zero rational number a,

a^m ÷ a^n = a^m-n

➲ If a and b are non - zero rational numbers and m is any integer, then

(a+b)^m = a^m × b^m

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