Exponents and Division Quiz

29 answers

1. Evaluate: 3^4 ÷ 3^2

Solution:
3^4 ÷ 3^2 = 81 ÷ 9 = 9

Answer: 9

2. Simplify: (2^3 x 3^2) ÷ (2^2 x 3^4)

Solution:
(2^3 x 3^2) ÷ (2^2 x 3^4) = (8 x 9) ÷ (4 x 81) = 72 ÷ 324 = 0.2222

Answer: 0.2222

3. Evaluate: 5^3 ÷ 5^3

Solution:
5^3 ÷ 5^3 = 1

Answer: 1

4. Simplify: (7^2 x 8^3) ÷ (7^2 x 2^3)

Solution:
(7^2 x 8^3) ÷ (7^2 x 2^3) = (49 x 512) ÷ (49 x 8) = 256

Answer: 256

5. Evaluate: (10^4) ÷ (2^6)

Solution:
(10^4) ÷ (2^6) = 10000 ÷ 64 = 156.25

Answer: 156.25
6. -2r(8r+5)
Solution:

Distribute -2r to 8r and 5 using the distributive property of multiplication:

-2r(8r + 5) = -2r(8r) + (-2r)(5)

= -16r^2 - 10r

Answer: -16r^2 -10r
4a(a^2+7a+4)
Solution:

Distribute 4a to a^2, 7a, and 4 using the distributive property of multiplication:

4a(a^2 + 7a + 4) = 4a(a^2) + 4a(7a) + 4a(4)

= 4a^3 + 28a^2 + 16a

Answer: 4a^3 + 28a^2 + 16a
(2y-3) (3y-2)
Solution:

Use the FOIL method to multiply the two binomials:

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

= 6y^2 - 4y - 9y + 6

Simplify by combining like terms:

= 6y^2 - 13y + 6

Answer: 6y^2 - 13y + 6
x^9/x^2
Solution:

To divide exponents with the same base, subtract the exponent in the denominator from the exponent in the numerator:

x^9 ÷ x^2 = x^(9-2) = x^7

Answer: x^7
did you use a single exponent for that problem
Yes, I used a single exponent (x^7) as the answer to the problem, because when dividing exponents with the same base, we subtract the exponent in the denominator from the exponent in the numerator to obtain a single exponent for the result.
ok do the same for h^14/h^5
Solution:

To divide exponents with the same base, we subtract the exponent in the denominator from the exponent in the numerator. Therefore,

h^14 / h^5 = h^(14-5) = h^9

Answer: h^9
Write each expression using a single exponent x⁹/x³
Solution:

To write the given expression with a single exponent, we have to subtract the exponent of the denominator from the exponent of the numerator.

x^9 / x^3 = x^(9-3) = x^6

Therefore, x⁹/x³ can be written as x^6 using a single exponent.

Answer: x^6
Write each expression using a single exponent x⁹/ x²
Solution:

To write the given expression with a single exponent, we have to subtract the exponent of the denominator from the exponent of the numerator.

x^9 / x^2 = x^(9-2) = x^7

Therefore, x⁹/ x² can be written as x^7 using a single exponent.

Answer: x^7
Simplify each expression: 4^4/4^6
Solution:

To simplify the given expression, we have to subtract the exponent of the denominator from the exponent of the numerator.

4^4 / 4^6 = 1 / 4^(6 - 4) = 1/4^2 = 1/16

Therefore, 4^4/4^6 simplifies to 1/16.

Answer: 1/16
Simplify each expression: 5^0 (1 point)

Replace the --- with <,>,or = to make a true statement. (1 point)
Solution:

Any number raised to the power of 0 is equal to 1. Therefore,

5^0 = 1

The statement 5^0 = 1 is a true statement.

Answer: 1

The statement 5^0 = 1 is true, so we can replace the --- with = to make a true statement.

Answer: =
Replace the --- with <,>,or = to make a true statement. (1 point)
7^4/7^2 ---- 49
Solution:

Using the rule for dividing exponents with the same base, we have:

7^4/7^2 = 7^(4-2) = 7^2 = 49

Therefore, 7^4/7^2 = 49 is a true statement.

Answer: =
Multiply the following polynomials (1 point)

-2r(8r+5)
Solution:

To multiply the given polynomials, we use the distributive property of multiplication:

-2r(8r + 5) = -2r(8r) - 2r(5)

= -16r^2 - 10r

Therefore, the product of the polynomials is -16r^2 - 10r.

Answer: -16r^2 - 10r
Multiply the following polynomials (1point)

4a(a^2+7a+4)
Solution:

To multiply the given polynomials, we use the distributive property of multiplication:

4a(a^2 + 7a + 4) = 4a(a^2) + 4a(7a) + 4a(4)

= 4a^3 + 28a^2 + 16a

Therefore, the product of the polynomials is 4a^3 + 28a^2 + 16a.

Answer: 4a^3 + 28a^2 + 16a
Multiply the following polynomials (1 point)

(2y-3)(3y-2)
Solution:

To multiply the given polynomials, we use the FOIL method:

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

= 6y^2 - 4y - 9y + 6

Simplifying by combining like terms, we get:

= 6y^2 - 13y + 6

Therefore, the product of the polynomials is 6y^2 - 13y + 6.

Answer: 6y^2 - 13y + 6