Exponents

Question 1

Exponent Rules:

What happens if a number is raised to the power of zero?

Answer 1

The answer is 1.

Example: 5⁰

=1

Question 2

​Exponent Rules:

What happens if a number is raised to the power of one?

Answer 2

The answer is the base

Example: 5¹

=5

Question 3

Exponent Rules:

If an exponent is to the power of a negative number, what do you do to solve it?

Answer 3

1) Make your exponent to a positive number
2) Turn your expoent into a fraction: 1/ your positive exponent
3) Solve your exponent

4) Your answer should look like this: 1/?

Example: 2^-1

1) 2¹
2) 1/ 2¹
3) 2¹= 2
4) 1/2

Question 4

Exponent Rules:

If a fraction is to the power of a negative number what steps do you take to solve it?

Answer 4

1) The negative exponent applies to both the top and bottom of the fraction
2) Make both of the exponents positive and turn them into 2 seperate fractions

3) Multiply the fractions

Example: (9/11)^-1

1) 9^-1/11^-1
2) 1/9¹ and 11¹/1
3) 1/9¹ X 11¹/1 = 11/9

Question 5

Multiplying Powers With The Same Base:

What do you do when multiplying powers with the same base?

Answer 5

Keep the base and add the exponents.

Example: 2²x2³

=2⁵

Question 6

Multiplying Powers With a Different Base:

What do you do when multiplying two powers with different bases?

Answer 6

Multiply the the coefficients and add the exponents.

Example: 2y³ x 3y⁵

=6y⁸

Question 7

Dividing Powers With The Same Base:

What happens when dividing powers with the same base?

Answer 7

Keep the base and subtract the exponents.

Example: a¹⁰/ a⁴

=a⁶

Question 8

Dividing Powers With a Different Base:

What do you do when dividing two powers with different bases?

Answer 8

Divide the coefficients and subtract exponents.

Example: 16b⁶/4b

=4b⁵

Question 9

A Fraction Raised To An Exponent:

What happens when you have a fraction in brackets with an exponent raised to it?

(1/4)²

Answer 9

The exponent is applied to both the numerator and denominator.

Example: 1/4²

1²/4²= 1/16

Question 10

Powers Raised To An Exponent:

What happens when you have an exponent in brackets with an exponent raised to it?

(2³)²

Answer 10

Keep the base and multiply the exponents.

Example: (2³)²

= 2⁶

Question 11

Multiplying Powers Raised to an Exponent:

What happens when there is 2 numbers being multiplied in brackets, raised to an exponent?

Answer 11

The exponent applies to both numbers being multiplied.

Example: (4X2)³

=4³X2³

⁼64X8

=512

Question 12

How do you find the greatest common factor of exponents?

Answer 12

Find how many of each base both numbers have in common

Example: 7³ and 7²

7x7x7

7x7

GCF= 7²