Indices Law

Question 1

2^3 x 2^4..

Answer 1

This is called the Product Law.
If the bases are the same, add the powers.

Answer:

2^3 x 2^4 = 2^3+4 = 2^7 = 128

Question 2

3^5 / 3^2..

Answer 2

This is called the Quotient Law.
If the bases are the same, subtract the powers.

Answer:

3^5 / 3^2 = 3^(5-2) = 3^3 = 27

Question 3

(2^3)^2..

Answer 3

This is called the Power of a Power Law.
Multiply the powers when raising a power to another power.

Answer:

(2^3)^2 = 2^3x2 = 2^6 = 64

Question 4

5^0..

Answer 4

This is called the Zero Power Law.
Any number raised to the power of zero is 1.

Answer:

5^0 = 1

Question 5

2^-3..

Answer 5

This is called the Negative Power Law.
A negative power means reciprocal.

Answer:

2^-3 = 1/2^3 = 1/8

Question 6

16^3/4..

Answer 6

This is called the Fractional Power Law.
The numerator 3 is the power, and the denominator 4 is the root.

Answer:

16^3/4 = (4√16)^3 = 2^3 = 8