What is exponents ?
The exponent of a number tells that how many times we use that number in a multiplication.
5³ = 5 ⋅ 5 ⋅ 5
Here 5 is base and 3 is called as power or exponent.
How to write the given product in exponential form ?
a ⋅ a ⋅ a ⋅ a = a⁴ (The variable a is multiplied 4 times itself. So, we write a and write 4 in the power)
a ⋅ a ⋅ c ⋅ c ⋅ c = a² ⋅ c³ (The variable a is multiplied 2 times and c is multiplied two times).
What is radical ?
In mathematics, a radical expression is defined as any expression containing a radical (√) symbol.
The exponential form of a n√a is a1/n
For example, ∛5 can be written in index form as
∛5 = 5 1/3
Basic Rules in Exponents and Radicals
Rules in Exponents :
xm ⋅ xn = x(m + n)
xm/xn = x(m – n)
(xm)n = xmn
x0 = 1
Rules in Radicals :
(n√a)n = a
n√a x n√b = n√(a x b)
n√a / n√b = n√(a / b)
(n√a)m = am/n