Question

If the expression 5¹⁰ was simplified using the power rule of exponents, which of the following would be an expanded equivalent expression?

A. (5 • 5)⁸
B. (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5)
C. (5¹⁶)⁶
D. (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The power rule of exponents states that when you raise a power to another power, you multiply the exponents. In this case, we have 5 raised to the 10th power, which means we have 5 multiplied by itself 10 times.

The expanded equivalent expression would be:

(5 • 5) • (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5)

Simplifying this expression, we get:

(25) • (25) • (25) • (25) • (25)

So the correct answer is:

B. (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5)

Answer 2

Which of the following is equivalent to 3^-⁴?

A. 1/3^-⁴
B. 1/81
C. -81
D. 81

Answer 3

[AI-generated answer — Bot GPT 3.5]

To simplify the expression 3^-⁴, we can apply the negative exponent rule, which states that any number raised to a negative exponent is equal to 1 divided by that number raised to the positive exponent.

Therefore, 3^-⁴ is equivalent to 1/3^⁴.

To further simplify, we can calculate 3^⁴.

3^⁴ is equal to 3 × 3 × 3 × 3, which is 81.

Therefore, 1/3^⁴ is equal to 1/81.

The correct answer is:

B. 1/81

Answer 4

Apply the property of negative integer exponents to find the numerical equivalent of 8^-³ . The answer should not contain any exponent expression or decimals.

8^-³=□

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the numerical equivalent of 8^-³ using the property of negative integer exponents, we can apply the following rule:

a^-n = 1/a^n

Using this rule, we can rewrite 8^-³ as 1/8³.

8³ is equal to 8 × 8 × 8, which is equal to 512.

Therefore, 1/8³ is equal to 1/512.

The numerical equivalent of 8^-³ is:

1/512

Answer 6

[AI-generated answer — Step-by-Step Bot]

If the expression 5¹⁰ is simplified using the power rule of exponents, we multiply the exponents:

5¹⁰ = 5^(1*10) = 5^10

Therefore, the expanded equivalent expression would be:

D. (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5)

Answer 7

[AI-generated answer — Explain Bot]

To simplify the expression 5^10 using the power rule of exponents, we need to remember that the power rule states that when we have a number raised to an exponent, and that entire expression is raised to another exponent, we multiply the exponents.

In this case, we have 5^10, which means 5 raised to the power of 10. If we want to expand this expression, we need to write it as a product of 5's.

Let's go through each option to determine which one represents an expanded equivalent expression:

A. (5 • 5)^8: This represents 2 5's raised to the power of 8. If we expand this, it becomes (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5). This is not an equivalent expression to 5^10.

B. (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5): This represents 5 raised to the power of 2, multiplied by itself 5 times. This would be (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5) • (5 • 5) = 25 • 25 • 25 • 25 • 25 = 25^5. This is not an equivalent expression to 5^10.

C. (5^16)^6: This represents 5 raised to the power of 16, and that entire expression raised to the power of 6. This can be expanded as 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5. This is not an equivalent expression to 5^10.

D. (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5): This represents 5 raised to the power of 5, multiplied by itself 5 times. This would be (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5) • (5 • 5 • 5 • 5 • 5) = 5^5 • 5^5 • 5^5 • 5^5 • 5^5 = 5^25. This is not an equivalent expression to 5^10.

None of the options provided represent an expanded equivalent expression to 5^10.