Product Law for Exponents:

Exponential notation or Power notation :
In a ^m , a is base m is called index or exponent or power
note : x^2 is x raised to power 2

Product Law: In multiplication , if base is same then add exponents.

a ^m * a ^n = a^ (m + n) where m, n are real terms and a not equal to zero
*This rule is applicable only when base is same

Example :simplify 2^ 5 * 2^ 6
2^ (5 + 6) = 2^11 ( using product law,here base is same )

practice : simplify
3^ 5 * 3^ 8
4^ 5 * 4 ^6
9^ 5 * 9 ^ 12

Answers:
3^13
4^11
9^17

Example :simplify x^ 6 * x^ 7
x^ (6 + 7) = x^13 ( using product law,here base is same )

practice: simplify
X * X^3 * X ^5 (note : x = x^1)
A^2 * A^4 * A^3 * A
n^2 * n^9 * n^23 * n^7

Answers:
X^9
A^10
n^41

Example : simplify x * y * y^ 2 * x^ 3
x * x^3 * y * y ^2 (first arrange the letters)
x^4 * Y^3 ( using product rule)

Practice: simplify
x^2 * y^2 * x^5 * y^6
x * y * x^4 * x^3 * y^5
k * y^2 * k^3 * k^2 * y^5

Answers:
x^7 * y^8
x^8 * y^6
k^6 * y 7