Which of the following is an equivalent expression to 5^9 • 5^-13 its only positive exponents that has been generated by applying the properties of integer exponents?
A. 1/5^4
B. 5^9/6^-12
C. 1/625
D. 5^4
To simplify the expression 5^9 • 5^-13, we can apply the property of exponents that states a^m • a^n = a^(m+n).
So, 5^9 • 5^-13 = 5^(9 + (-13)) = 5^-4.
Therefore, the equivalent expression that only has positive exponents is 5^4.
The correct answer is D. 5^4.
Which property of exponents we used to generate the equivalent expression 3^14 from 3^5/3^-9
A. Only the product rule of exponents
B. Only the power rule of exponents
C. The property of negative exponents and product rule of exponents.
D. Only the property of negative exponents.
To generate the equivalent expression 3^14 from 3^5/3^-9, we can apply both the property of negative exponents and the product rule of exponents.
First, we can use the property of negative exponents, which states that a^(-n) = 1/a^n. Thus, 3^-9 = 1/3^9.
Next, we can use the product rule of exponents, which states that a^m / a^n = a^(m-n). Applying this rule to 3^5/3^9, we get 3^(5-9) = 3^-4.
Finally, we can simplify further using the property of negative exponents again. 3^-4 = 1/3^4 = 1/81.
Therefore, the equivalent expression 3^14 is generated using the properties of negative exponents and the product rule of exponents.
The correct answer is C. The property of negative exponents and product rule of exponents.
Which of the following is an equivalent expression to 15^0•7^-2/(-4)^-3 how many positive exponents that has been generated by applying to properties of integer exponents
A. 1/7^2•(-4)^-3
B. 4^3/7^2
C. (-4)^3/7^2
D. 7^2/(-4)^3
To simplify the expression 15^0•7^-2/(-4)^-3, we can apply the property of any number raised to the power of 0 is equal to 1.
Therefore, 15^0 is equal to 1.
Next, we can apply the property of negative exponents, which states that a^(-n) = 1/a^n.
So, 7^-2 is equal to 1/7^2.
Similarly, (-4)^-3 is equal to 1/(-4)^3.
Combining all the terms, we have 1 • 1/7^2 • 1/(-4)^3.
Simplifying further, we have 1/7^2 • 1/(-4)^3.
Therefore, the equivalent expression that only has positive exponents is 1/7^2 • (-4)^3.
The correct answer is A. 1/7^2 • (-4)^3.
There is only one positive exponent generated by applying the properties of integer exponents, which is 3 in (-4)^3.
Thus, the number of positive exponents generated is 1.
Which of the following is the equivalent expression to (15^-3•4^7)^0/4^-3 that has been generated by applying the properties of integer exponents
A. 64.
B. 60/4^-3
C. 1 • 4^-3
D. 1/64
To find an equivalent expression to 5^9 • 5^-13 with only positive exponents, we can apply the properties of integer exponents.
The property we can use here is the product rule: a^m • a^n = a^(m+n).
So, let's apply this rule to the given expression: 5^9 • 5^-13 = 5^(9 + (-13)) = 5^-4.
To write this expression with only positive exponents, we can use another property of exponents: a^-n = 1/a^n.
Applying this property, we can rewrite 5^-4 as 1/5^4.
So, the equivalent expression with only positive exponents is 1/5^4.
Therefore, the answer is option A.