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
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.
Which of the following is equivalent to 6^-2
A. 1/6^-2
B. 36
C. 1/36
D. 1/2^6
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.
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
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.
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
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.
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
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.
To determine which of the options is equivalent to 1/8^5, we need to simplify the given expression.
Starting with 1/8^5, we can rewrite 8^5 as (2^3)^5 using the rule of exponentiation that states (a^b)^c = a^(b*c).
Therefore, 8^5 can be simplified as 2^(3*5) which equals 2^15.
So, 1/8^5 can be further simplified as 1/(2^15).
To simplify this expression, we use the rule of negative exponents, which states that a^(-b) is equal to 1/a^b.
Applying this rule, we can rewrite 1/(2^15) as 2^(-15), which means the expression 1/8^5 is equivalent to 2^(-15).
Now let's check which option is equivalent to 2^(-15):
A. 8^5: Since 8^5 is equal to 2^(3*5), it is not equivalent to 2^(-15). So, option A is not the answer.
B. 8 1/5: This option is not a valid exponent expression, so it is not equivalent to 2^(-15). Thus, option B is not the answer.
C. 8^-5: Since 8^-5 is equal to 1/8^5, it is equivalent to 2^(-15). Therefore, option C is the answer.
D. 5^-8: This option does not involve 2 as the base and does not match the simplified expression 2^(-15). Hence, option D is not the answer.
Therefore, the correct answer is option C.