Simplifying Radical Expressions Assignment

1) Which choice represents the expression below as a single exponential expression? 2¹¹ * 2⁵

2^16 * 2^16

2^16

2^55

2^6

The expression 211 * 25 can be simplified by writing both numbers as powers of 2. Since 211 is not a power of 2, we cannot simplify it further. However, 25 can be written as 2^5. Therefore, the expression becomes 2^11 * 2^5. Using the rule of exponents, we can add the exponents when multiplying powers with the same base. So, 2^11 * 2^5 simplifies to 2^(11+5) which is equal to 2^16.

Explanation

The expression 211 * 25 can be simplified by writing both numbers as powers of 2. Since 211 is not a power of 2, we cannot simplify it further. However, 25 can be written as 2^5. Therefore, the expression becomes 2^11 * 2^5. Using the rule of exponents, we can add the exponents when multiplying powers with the same base. So, 2^11 * 2^5 simplifies to 2^(11+5) which is equal to 2^16.

2) Which choice represents the expression below as a single exponential expression? 6⁵ * 6³

6^8 * 6^8

6^15

6^2

6^8

The correct answer is 6^8. The expression 65 * 63 can be written as 6^8 because both numbers 65 and 63 can be expressed as powers of 6. By multiplying the powers together, we get 6^8.

Explanation

The correct answer is 6^8. The expression 65 * 63 can be written as 6^8 because both numbers 65 and 63 can be expressed as powers of 6. By multiplying the powers together, we get 6^8.

3) Which choice represents the expression below as a single exponential expression? y⁸ * y³

Y^5

Y^24

Y^11 * 4y11

Y^11

The given expression can be simplified by adding the exponents when multiplying variables with the same base. In this case, y^8 * y^3 = y^(8+3) = y^11. Therefore, the expression y^8 * y^3 can be represented as y^11, which is the correct answer.

Explanation

The given expression can be simplified by adding the exponents when multiplying variables with the same base. In this case, y^8 * y^3 = y^(8+3) = y^11. Therefore, the expression y^8 * y^3 can be represented as y^11, which is the correct answer.

4) Which choice represents the expression below as a single exponential expression? x⁹ * x⁷

X^16 * x^16

X^63

X^2

X^16

The correct answer is x^16 because when multiplying two exponential expressions with the same base, you add the exponents. In this case, x^9 * x^7 becomes x^(9+7) which simplifies to x^16.

Explanation

The correct answer is x^16 because when multiplying two exponential expressions with the same base, you add the exponents. In this case, x^9 * x^7 becomes x^(9+7) which simplifies to x^16.

5) Use the Multiplication Law of Exponents to simplify the exponential expression below. a¹⁰⁰ * a³⁰⁰

A^300

A^500

A^30

A^400

The Multiplication Law of Exponents states that when multiplying two exponential expressions with the same base, you can add the exponents. In this case, we are multiplying a^100 and a^300, both with the base a. Therefore, we can add the exponents 100 and 300 to get 400. So, the simplified exponential expression is a^400.

Explanation

The Multiplication Law of Exponents states that when multiplying two exponential expressions with the same base, you can add the exponents. In this case, we are multiplying a^100 and a^300, both with the base a. Therefore, we can add the exponents 100 and 300 to get 400. So, the simplified exponential expression is a^400.

6) The Multiplication Law of Exponents says that for any numbers b, n, and m, bⁿ * b^m = b^{n + m}.

True

False

The explanation for the given correct answer is that the Multiplication Law of Exponents states that when multiplying two numbers with the same base, you can add their exponents. In this case, the law is applied to the expression bn * bm, where b is the base and n and m are the exponents. By applying the law, we can rewrite the expression as bn+m. Therefore, the statement is true.

Explanation

The explanation for the given correct answer is that the Multiplication Law of Exponents states that when multiplying two numbers with the same base, you can add their exponents. In this case, the law is applied to the expression bn * bm, where b is the base and n and m are the exponents. By applying the law, we can rewrite the expression as bn+m. Therefore, the statement is true.

7) Which one do you like?

Option 1

Option 2

Option 3

Option 4

The given question asks for the preference of the person. Since there is no additional context provided, it is impossible to determine the reason behind the preference. Therefore, any of the options could be the correct answer depending on the individual's personal taste and preference.

Explanation

The given question asks for the preference of the person. Since there is no additional context provided, it is impossible to determine the reason behind the preference. Therefore, any of the options could be the correct answer depending on the individual's personal taste and preference.