Powers And Exponents

Question 0

Basic rules of exponents:

Raising to the zero power

Answer 0

For any non-zero number a

a^0=1
6^0=1

Question 1

Basic rules of exponents:

Raising to the first power

Answer 1

For any non-zero number a

a^1=a

6^1=6

Question 2

Basic rules of exponents:

Negative exponents

Answer 2

For any non-zero number a and integer n

a^-n=1/a^n

6^-2=1/6^2=1/36
2/4^-3=2x4^3=1x64=128

Question 3

Advanced rules of exponents:

Multiplying numbers with same base

Answer 3

Add exponents when multiplying numbers with the same base

a^m * a^n = a^m+n

x^5 * x^8= x^13

Question 4

Advanced rules of exponents:

Raising a power to a power

Answer 4

Multiply the exponents when a power is raised to a power

(a^m)^n= a^mn

(x^5)^2=x^10

Question 5

Advanced rules of exponents:

Raising a product to a power

Answer 5

Each of the products is separately raised to the power

(ab) ^n = a^n * b^n
(5x) ^3 = 5^3 * x^3 = 125x^3

Question 6

Advanced rules of exponents:

Raising a quotient to a power

Answer 6

Each part of the quotient is separately raised to the power

(a/b)^n = a^n/b^n

(x/5)^3 = x^3/5^3 = x^3/125

Question 7

What is the opposite operation of raising a number to a power?

Answer 7

Taking its root. Square root is most familiar.

Question 8

What are fractional powers most similar to?

Answer 8

Finding roots. The denominator of a fractional power tells you what root to find. Then multiply the root by the numerator if other that one.

Ex: 32^3/5 = ?
32^1/5=2. (2x2x2x2x2 =32)
2x2x2=8

Question 9

Convert this number to scientific notation:

587,980

Answer 9

5.8798 x 10^5

Question 10

Convert this number to scientific notation

0.00259

Answer 10

2.59 x 10^-3

Numbers between 0 and 1 have negative exponents