Index & Expanded Form, Powers & Roots

How do you use exponents to represent numbers?

• repeated multiplication

• repeated addition

• repeated subtraction

• repeated division

Answer explanation

Exponents are used to represent numbers through repeated multiplication, where a number is multiplied by itself a certain number of times.

Write 6 x 6 x 6 in index form.

• 6³

• 216

• 3 x 6

• 3⁶

Answer explanation

To write 6 x 6 x 6 in index form, we use the exponent notation, which is 6^3. Therefore, the correct index form is 6^3.

Write in index notation. 2 x 3 x 3 x 5 x 5 x 5 x 2

• 2 x 3² x 5²

• 2² + 3² + 5³

• 2² x 3² x 5³

Answer explanation

The correct index notation for 2 x 3 x 3 x 5 x 5 x 5 x 2 is 2^2 x 3^2 x 5^3.

Write in index notation. 7 x 7 x 7 x 7 x 7 x 10

• 7⁵ + 10

• 7⁵ x 10

• 5⁷ x 1¹⁰

Answer explanation

The correct choice is 7^5 x 10 because the expression is written in index notation, where 7^5 represents 7 multiplied by itself 5 times, and then multiplied by 10.

Which is equivalent to 5 x 5 x 5 x 5

• 5³

• 5⁴

• 4⁵

• 5⁵

Answer explanation

To find the equivalent of 5 x 5 x 5 x 5, we multiply the numbers together, resulting in 5^4.

The exponent tells me...

• the answer

• the trick

• the number of times to multiply the base (factor)

• The number of days in a week

Answer explanation

The exponent tells me the number of times to multiply the base (factor)

Which is the base and which is the exponent? 5²

• 5 is base and 2 is exponent

• 5 is base and exponent

• 2 is base and 5 is exponent

• 2 is base and exponent

Answer explanation

In the expression 5^2, 5 is the base and 2 is the exponent. The base is the number being raised to a power, while the exponent indicates how many times the base is multiplied by itself.

24⁷ , in this example 7 is the _____________

• base

• exponent

Answer explanation

The correct term for the number that indicates how many times the base number is multiplied by itself is the exponent, as in 24^7.

Which number is the BASE?

2³

• 2

• 3

• 8

• not here

Answer explanation

The BASE in the expression 2^3 is 2 because it is the number being raised to the power of 3.

Which number is the EXPONENT?

4²

• 4

• 2

• 16

• not here

Answer explanation

The EXPONENT in the expression 4^2 is the number 2, which represents the power to which the base number 4 is raised.