Question

There are many properties of exponents. These properties are used to make problems with exponents simpler. 1] Choose one of the properties and explain why it isbtrue. Then write a numerical expression and use the property you chose to simplify the expression.​

Answer 1

a^m × a^n = a^(m+n)

means that when you take a number, a, multiplied by itself m times, and multiply that by the same number a multiplied by itself n times, it's the same as taking that number a and raising it to a power equal to the sum of m and n.

To prove this, we can verify it numerically:

Let us take,

a = 10

m = 2

n = 5

Now,

10² × 10⁵ = 10²+⁵

100 × 100000 = 10⁷

10000000 = 10000000

Another example,

Let us take,

a = 2

m = 0

n = 3

Now,

2⁰ × 2³ = 2⁰+³

1 × 8 = 2³

8 = 8