Question

Simplify the following:

What is 6^3 x 6^4?
a) 6^7
b) 6^12
c) 6^25
d) 6^43

What is 42^21 / 42^19?
a) 42^2
b) 1
c) 42^40
d) 42^19

What is 4^3 x 4^2 x 4^4?
a) 4^9
b) 4^12
c) 4^24
d) 4^81

What is (2^2)^3?
a) 2^6
b) 8
c) 2^5
d) 2^9

What is (2^2 x 3^4) x (3^2 x 2^4)?
a) 2^6 x 3^6
b) 12^4
c) 2^8 x 3^6
d) 2^6 x 3^8

What is 7^9 / 7^7?
a) 7^2
b) 7^16
c) 49
d) 7^63

Write 2.1 x 10^-3 in standard form.
a) 210
b) 0.0021
c) 21
d) 0.00021

Write 0.000033 in scientific notation.
a) 3.3 x 10^-5
b) 3.3 x 10^-6
c) 33 x 10^-5
d) 33 x 10^-6

Write 4,343,100 in scientific notation.
a) 4.3431 x 10^6
b) 43.431 x 10^5
c) 4.3431 x 10^7
d) 43431 x 10^3

Answer 1

1. a) 6⁷

2. b) 1

3. a) 4⁹

4. a) 2⁶

5. c) 2⁸x 3⁶

6. a) 7²

7. b) 0.0021

8. a) 3.3 x 10⁻⁵

9. a) 4.3431 x 10⁶

Step-by-step explanation:

For the first question, 6³ x 6⁴ can be simplified by adding the exponents since the bases are the same. Therefore, 6³ x
`6^4` =
`6^(^3^+^4^)` = 6⁷.

In the second question,
`42^2^1` /
`42^1^9` simplifies to
`42^(^2^1^-^1^9^)` = 42², as we subtract the exponents when dividing with the same base.

For the third question, 4³ x 4² x 4⁴ simplifies to
`4^(^3^+^2^+^4^)` = 4⁹, as we add the exponents when multiplying with the same base.

In the fourth question, (2²)³ simplifies to 2²*³ = 2⁶, as we multiply the exponent outside the parentheses with the exponent inside.

The fifth question involves multiplying two expressions, resulting in (2² x 3⁴) x (3² x 2⁴). By combining like terms, we get 2⁶ x 3⁶.

The sixth question, 7⁹ / 7⁷ simplifies to 7⁹⁻⁷ = 7², subtracting the exponents when dividing.

Moving to the seventh question, 2.1 x 10⁻³ in standard form is written as 2.1 x 10⁻³.

For the eighth question, 0.000033 in scientific notation is expressed as 3.3 x 10⁻⁵.

Lastly, the number 4,343,100 in scientific notation is represented as 4.3431 x 10⁶.