Question

3^3 / 3^6

Answer 1

3^3 / 3^6 is equal to 1/3^3 * 1/3^3 * 1/3^3 * 3^3.

Using the rules of exponents, we can simplify this:

1/3^3 * 1/3^3 * 1/3^3 * 3^3 = 1/3^(3+3+3) * 3^3

= 1/3^9 * 27

= 1/19683

Therefore, 3^3 / 3^6 = 1/19683.

Answer 2

3^3 / 3^6

1/ 27
1/9
9
-27

Answer 3

The answer is:

1/27

Answer 4

(1.4 x 10 ^1) (8 x 10 ^4)
9.4 x 10^4
9.4 x 10^5
1.12 x 10^5
1.12 x 10^6

Answer 5

When multiplying two numbers written in scientific notation, we need to multiply the decimal parts separately and add the exponents.

(1.4 x 10^1) (8 x 10^4) = (1.4)(8) x 10^(1+4) = 11.2 x 10^5 = 1.12 x 10^6

Therefore, the answer is 1.12 x 10^6.

Answer 6

(1.17 x10 ^-4 ) 5 x 10^-5)
8.5 x 10 ^-9
8.5 x 10^20
6.7 x 10^-9
6.7 x 10^20

Answer 7

To multiply two numbers in scientific notation, we multiply the decimal parts and add the exponents.

(1.17 x 10^-4) (5 x 10^-5) = (1.17 x 5) x 10^(-4-5) = 5.85 x 10^-9

Therefore, the answer is 5.85 x 10^-9, which is not one of the options provided. So the possible options contain a typo.

The closest option we have is 6.7 x 10^-9, but that is not equal to the exact result of the multiplication.

Answer 8

8t ^5 x 8t^5
64t^25
64t^10
16t^10
16t^5

Answer 9

When multiplying two terms with the same base, we add the exponents.

8t^5 x 8t^5 = (8 x 8) t^(5+5) = 64t^10

Therefore, the answer is 64t^10.

Answer 10

-x (5x - 4)

Answer 11

We can use the distributive property of multiplication to simplify the expression:

-x (5x - 4) = -x (5x) - x(-4) = -5x^2 + 4x

Therefore, -x (5x - 4) simplifies to -5x^2 + 4x.

Answer 12

5k^2 (-6k^2 - 2k + 6)

Answer 13

We can use distributive property of multiplication and multiply each term inside the parentheses by 5k^2:

5k^2 (-6k^2 - 2k + 6) = -30k^4 - 10k^3 + 30k^2

Therefore, the simplified form of 5k^2 (-6k^2 - 2k + 6) is -30k^4 - 10k^3 + 30k^2.

Answer 14

(2k + 3 ) ( k- 1)

Answer 15

We can use the distributive property of multiplication to simplify the expression:

(2k + 3)(k - 1) = 2k(k) + 2k(-1) + 3(k) + 3(-1)

= 2k^2 - 2k + 3k - 3

= 2k^2 + k - 3

Therefore, the simplified form of (2k + 3)(k - 1) is 2k^2 + k - 3.

Answer 16

(-2y + 5 ) ( y + 3)

Answer 17

We can use the distributive property of multiplication to simplify the expression:

(-2y + 5)(y + 3) = -2y(y) - 2y(3) + 5(y) + 5(3)

= -2y^2 - 6y + 5y + 15

= -2y^2 - y + 15

Therefore, the simplified form of (-2y + 5)(y + 3) is -2y^2 - y + 15.

Answer 18

3^4/ 3^4

Answer 19

3^4/3^4 is equal to 1, because any non-zero number raised to the power of zero is 1.

Alternatively, we can use the quotient rule of exponents, which states that when dividing two powers with the same base, we can simply subtract the exponents:

3^4/3^4 = 3^(4-4) = 3^0 = 1

Therefore, 3^4/3^4 is equal to 1.

Answer 20

x^16 / x^3

Answer 21

When dividing with the same base, we can subtract the exponents:

x^16 / x^3 = x^(16-3) = x^13

Therefore, x^16 / x^3 simplifies to x^13.

Answer 22

100^12 / 100^8

Answer 23

When dividing with the same base, we can subtract the exponents:

100^12 / 100^8 = 100^(12-8) = 100^4

Therefore, 100^12 / 100^8 simplifies to 100^4.

Answer 24

7x^2 - x - 2 - 6x^3 + 3

Answer 25

We can combine like terms by adding or subtracting coefficients of the same degree:

7x^2 - x - 2 - 6x^3 + 3 = -6x^3 + 7x^2 - x + 1

Therefore, the simplified form of 7x^2 - x - 2 - 6x^3 + 3 is -6x^3 + 7x^2 - x + 1.

Answer 26

4x^2 + 8x - 11x + 6 - 5x^2 + 2

Answer 27

We can combine like terms by adding or subtracting coefficients of the same degree:

4x^2 + 8x - 11x + 6 - 5x^2 + 2 = (4x^2 - 5x^2) + (8x - 11x) + (6 + 2)

= -x^2 - 3x + 8

Therefore, the simplified form of 4x^2 + 8x - 11x + 6 - 5x^2 + 2 is -x^2 - 3x + 8.

Answer 28

2x^2 + 8 - 4x + 3x - 6x^2 +7

Answer 29

We can combine like terms by adding or subtracting coefficients of the same degree:

2x^2 + 8 - 4x + 3x - 6x^2 + 7 = (2x^2 - 6x^2) + (-4x + 3x) + (8 + 7)

= -4x^2 - x + 15

Therefore, the simplified form of 2x^2 + 8 - 4x + 3x - 6x^2 + 7 is -4x^2 - x + 15.