Question

Which of the following is developed to be equivalent to 1/8^5
A. 8^5
B. 8 1/5
C. 8^-5
D. 5^-8

Answer 1

Which of the following is equivalent to 6^-2

A. 1/6^-2
B. 36
C. 1/36
D. 1/2^6

Answer 2

Which of the following is an equivalent expression to 13^-5 • 13^-11 with only positive exponents, generated by applying the properties of exponents?
A. 1/26^16
B. 1/13^6
C. 1/26^6
D. 1/13^16

Answer 3

Which of the following is an equivalent expression to 14^-7/9^-13 with only positive exponents, generated by applying the property of negative integer exponents?
A. 14^-7 • 9^13
B. 1/9^13•14^-7
C. 14^7/9^13
D. 9^13/14^7

Answer 4

Which of the following is an equivalent expression to 7^3/25^-4 with only positive exponents generated by applying the property of negative integer exponents
A.7^3 • 25^4
B. 25^4/7^-3
C. 25^4/7^3
D. 7^3/25^4

Answer 5

The correct answer is C. 8^-5.

To understand why, let's simplify 1/8^5 step by step:

1/8^5 = 1/((2^3)^5)
= 1/(2^(3*5))
= 1/2^15
= (2^(-1))^15
= 2^(-15)
= 8^(-5)

Therefore, 1/8^5 is equivalent to 8^-5.

Answer 6

The correct answer is A. 1/6^-2.

To understand why, let's simplify 6^-2 step by step:

6^-2 = 1/(6^2)
= 1/(6 * 6)
= 1/36

Therefore, 6^-2 is equivalent to 1/36.
So the correct choice is A. 1/6^-2.

Answer 7

To simplify the expression 13^-5 • 13^-11 and generate an equivalent expression with positive exponents, we can use the property of exponents that states when multiplying two numbers with the same base, you add the exponents.

So, 13^-5 • 13^-11 = 13^(-5+(-11)) = 13^-16

To further simplify and change the exponent to positive, we can use the property of exponents that states when a number with a negative exponent is moved to the denominator, the exponent becomes positive.

Therefore, 13^-16 can be rewritten as 1/13^16.

So, the correct answer is D. 1/13^16.

Answer 8

To simplify the expression 14^-7/9^-13 and generate an equivalent expression with positive exponents using the property of negative integer exponents, we can reciprocate the fractions with negative exponents and change the signs of the exponents.

So, 14^-7/9^-13 is equivalent to (1/14^7) • (1/9^(-13)).

Recall that when a number with a negative exponent is moved to the denominator, the exponent becomes positive.

Therefore, (1/14^7) • (1/9^(-13)) can be rewritten as (1/14^7) • (9^13).

So, the correct answer is B. 1/9^13•14^-7.

Answer 9

To simplify the expression 7^3/25^-4 and generate an equivalent expression with positive exponents using the property of negative integer exponents, we can reciprocate the fraction with the negative exponent and change the sign of the exponent.

So, 7^3/25^-4 is equivalent to 7^3 • 25^4.

Therefore, the correct answer is A. 7^3 • 25^4.