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
Exponents and Division Quiz
29 answers
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
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
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
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
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
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
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
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
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)
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: =
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
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: =
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)
-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
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)
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
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)
(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
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