Which of the following is an equivalent expression to 5^9⋅5^−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
1/625
Start Fraction 1 over 625 end fraction
1/5^4
Start Fraction 1 over 5 superscript 4 baseline end fraction
5^4
5 superscript 4 baseline
5^9/5^−13
7 answers
The equivalent expression with only positive exponents would be 5^(9+(-13)), which simplifies to 5^(-4). So, the correct answer is 1/5^4.
Which property of exponents was used to generate the equivalent expression 3^14 from 3^5/3^−9?(1 point)
Responses
only the Product Rule of Exponents
only the Product Rule of Exponents
only the Property of Negative Exponents
only the Property of Negative Exponents
only the Power Rule of Exponents
only the Power Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
Responses
only the Product Rule of Exponents
only the Product Rule of Exponents
only the Property of Negative Exponents
only the Property of Negative Exponents
only the Power Rule of Exponents
only the Power Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
The property that was used to generate the equivalent expression 3^14 from 3^5/3^(-9) is the Property of Negative Exponents.
Which of the following is an equivalent expression to 15^0 ⋅ 7^−2 (−4)^−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
7^2(−4)^3
Start Fraction 7 squared over left parenthesis negative 4 right parenthesis cubed end fraction
4^3/7^2
Start Fraction 4 cubed over 7 squared end fraction
(−4)^3/7^2
start fraction left parenthesis negative 4 right parenthesis cubed over 7 squared end fraction
1/7^2 ⋅ (−4)^−3
Responses
7^2(−4)^3
Start Fraction 7 squared over left parenthesis negative 4 right parenthesis cubed end fraction
4^3/7^2
Start Fraction 4 cubed over 7 squared end fraction
(−4)^3/7^2
start fraction left parenthesis negative 4 right parenthesis cubed over 7 squared end fraction
1/7^2 ⋅ (−4)^−3
To find the equivalent expression with only positive exponents, we need to apply the property of negative exponents.
We know that any number raised to the power of 0 is equal to 1. So, 15^0 is equal to 1.
Also, using the property of negative exponents, we can rewrite 7^(-2) as 1/7^2 and (-4)^(-3) as 1/(-4)^3.
Therefore, the equivalent expression with only positive exponents is 1/7^2 ⋅ 1/(-4)^3.
So, the correct answer is 1/7^2 ⋅ (−4)^−3.
We know that any number raised to the power of 0 is equal to 1. So, 15^0 is equal to 1.
Also, using the property of negative exponents, we can rewrite 7^(-2) as 1/7^2 and (-4)^(-3) as 1/(-4)^3.
Therefore, the equivalent expression with only positive exponents is 1/7^2 ⋅ 1/(-4)^3.
So, the correct answer is 1/7^2 ⋅ (−4)^−3.
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?(1 point)
Responses
1/64
Start Fraction 1 over 64 end fraction
64
1⋅4^−3
1 times 4 negative cubed
60/4^−3
Responses
1/64
Start Fraction 1 over 64 end fraction
64
1⋅4^−3
1 times 4 negative cubed
60/4^−3
To find the equivalent expression using the properties of integer exponents, we need to simplify the given expression.
First, we can simplify the expression inside the parentheses: (15^(-3) ⋅ 4^7) = (1/15^3 ⋅ 4^7). This is because any number, except 0, raised to the power of -n can be written as 1 divided by that number raised to the power of n.
Now, we can simplify the expression with the exponent of 0: (1 / 15^3 ⋅ 4^7)^0 = 1. This is because any number raised to the power of 0 is equal to 1.
Finally, we simplify the numerator and denominator with the exponent of -3: 1/4^(-3) = 4^3. This is because any number raised to the power of -n can be written as the reciprocal of that number raised to the power of n.
Therefore, the equivalent expression is 4^3, which is equal to 64. So, the correct answer is 64.
First, we can simplify the expression inside the parentheses: (15^(-3) ⋅ 4^7) = (1/15^3 ⋅ 4^7). This is because any number, except 0, raised to the power of -n can be written as 1 divided by that number raised to the power of n.
Now, we can simplify the expression with the exponent of 0: (1 / 15^3 ⋅ 4^7)^0 = 1. This is because any number raised to the power of 0 is equal to 1.
Finally, we simplify the numerator and denominator with the exponent of -3: 1/4^(-3) = 4^3. This is because any number raised to the power of -n can be written as the reciprocal of that number raised to the power of n.
Therefore, the equivalent expression is 4^3, which is equal to 64. So, the correct answer is 64.