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)

5 answers

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)
Which of the following is equivalent to 3^-⁴?
A. 1/3^-⁴
B. 1/81
C. -81
D. 81
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
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=□
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