which of the following is developed to be equivalent to 1/8^5?
a. 8^-5
b. 5^-8
c. 8 1/5
d. 8^5
To find an equivalent expression to 1/8^5, we can rewrite 1/8^5 as (8^-1)^5.
By the power of a power rule, we can simplify (8^-1)^5 as 8^(-1*5), which is equal to 8^-5.
Therefore, the equivalent expression to 1/8^5 is a. 8^-5.
which of the following is equivalent to 6^-2?
a. 1/36
b. 36
c. 1/6^-2
d. 1/2^6
To simplify 6^-2, we can rewrite it as 1/6^2 using the definition of a negative exponent.
6^2 is equal to 36, so 1/6^2 is equal to 1/36.
Therefore, the equivalent expression to 6^-2 is a. 1/36.
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. 1/26^6
c. 1/13^6
d. 1/13^16
To simplify 13^-5 . 13^-11 with positive exponents, we can apply the property of exponents that states "When multiplying powers with the same base, add the exponents."
Using this property, we can rewrite 13^-5 . 13^-11 as 13^(-5 + -11).
Adding the exponents, we get 13^-16.
To convert this into an expression with only positive exponents, we can rewrite it as 1/13^16.
Therefore, the equivalent expression with only positive exponents 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. 9^13/14^7
b. 14^-7 . 9^13
c. 1/9^13 . 14^-7
d. 14^7/9^13
To simplify 14^-7/9^-13 with positive exponents, we can apply the property of negative integer exponents which states "When an expression with a negative exponent is in the denominator, move it to the numerator and change the sign of the exponent."
Applying this property, we can rewrite 14^-7/9^-13 as (9^13)/(14^7).
Therefore, the equivalent expression with only positive exponents is a. 9^13/14^7.