Please let me know if i answered these correctly thanks
1.Which property of the real numbers is illustrated by the following statement?
4(3x) = (4 ∙ 3)x
answer: distributive property
2. Which property of the real numbers is illustrated by the following statement?
8(c + ax) + 0 = 8(c + ax)
answer: Associative property of addition
3.Write in rational exponent form. Do not simplify. -√175
answer: 175 ^–1/2
4. 36x^4 y^16
answer: 18x^2 y^8
5√243a^25 b^5
answer: 3a^5 b
1. Correct! The statement 4(3x) = (4 ∙ 3)x illustrates the distributive property of the real numbers.
2. Incorrect. The correct answer is the identity property of addition. The statement 8(c + ax) + 0 = 8(c + ax) shows that when you add 0 to any number, it remains unchanged.
3. Incorrect. The correct answer is (-175)^(1/2), not 175^(-1/2). The negative sign should be included in the exponent.
4. Correct! The expression 36x^4 y^16 can be simplified to 18x^2 y^8.
5. Incorrect. The correct answer is 3a^5 b^5. When you take the fifth root of 243a^25 b^5, both the coefficients and the exponents inside the root remain unchanged.
1. You answered correctly. The property illustrated by the statement is the distributive property.
To verify this, you can apply the distributive property:
4(3x) = 4 * 3 * x = 12x
and
(4 ∙ 3)x = 12x
Since both sides of the equation simplify to the same expression (12x), the distributive property is confirmed.
2. You answered incorrectly. The property illustrated by the statement is the identity property of addition.
To verify this, let's break down the statement:
8(c + ax) + 0 = 8(c + ax)
In this case, the "0" acts as the additive identity. Adding 0 to any number doesn't change its value. Therefore, the statement shows that adding 0 to (8(c + ax)) doesn't alter the expression.
3. You answered correctly. To write -√175 in rational exponent form, you can express it as 175 raised to the power of -1/2.
The exponent -1/2 indicates that you are taking the reciprocal (negative exponent) of the square root (exponent 1/2) of 175.
4. You answered incorrectly. The expression 36x^4 y^16 cannot be simplified to 18x^2 y^8.
To simplify this expression, you need to divide the coefficients and reduce the exponents:
36x^4 y^16 = (6 * 6) * (x^2 * x^2) * (y^8 * y^8)
= 6^2 * x^(4 + 4) * y^(16 + 16)
= 36x^8 y^32
So, the simplified form is 36x^8 y^32.
5. You answered incorrectly. The expression 5√243a^25 b^5 can be simplified further.
To simplify this radical expression, you can break down the radicand (243) into its prime factors:
243 = 3 * 3 * 3 * 3 * 3 = 3^5
Now, let's simplify the expression:
5√243a^25 b^5 = 5 * √(3^5) * a^25 * b^5
= 5 * (3^(5/2)) * a^25 * b^5
Therefore, the simplified form is 5 * 3^(5/2) * a^25 * b^5.
4. √36x^4 y^16
answer: 18x^2 y^8
#5
5√243a^25 b^5
answer: 3a^5 b