The expression 5^9⋅5^−13 can be simplified using the property of exponents which states that when multiplying terms with the same base, you add their exponents:
5^9⋅5^−13 = 5^(9+(-13)) = 5^(-4)
The equivalent expression with only positive exponents is 1/5^4.
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)
8 answers
Which property of exponents was used to generate the equivalent expression 3^14 from 3^5/3^−9?(1 point)
Responses
only the Power Rule of Exponents
only the Power Rule of Exponents
only the Property of Negative Exponents
only the Property of Negative Exponents
only the Product Rule of Exponents
only the Product 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 Power Rule of Exponents
only the Power Rule of Exponents
only the Property of Negative Exponents
only the Property of Negative Exponents
only the Product Rule of Exponents
only the Product 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 of exponents that was used to generate the equivalent expression 3^14 from 3^5/3^−9 is the Property of Negative Exponents. By applying this property, we can rewrite the expression 3^−9 as 1/3^9. Then, using the Product Rule of Exponents, we can simplify 3^5/3^−9 to 3^5 * 1/3^9, which can be further simplified to 3^(5-9) = 3^(-4) = 1/3^4 = 1/81.
Which of the following is an equivalent expression to 150 ⋅ 7−2 (−4)−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
4372
Start Fraction 4 cubed over 7 squared end fraction
172 ⋅ (−4)−3
Start Fraction 1 over 7 squared times left parenthesis negative 4 right parenthesis superscript negative 3 baseline End Fraction
72(−4)3
Start Fraction 7 squared over left parenthesis negative 4 right parenthesis cubed end fraction
(−4)372
Responses
4372
Start Fraction 4 cubed over 7 squared end fraction
172 ⋅ (−4)−3
Start Fraction 1 over 7 squared times left parenthesis negative 4 right parenthesis superscript negative 3 baseline End Fraction
72(−4)3
Start Fraction 7 squared over left parenthesis negative 4 right parenthesis cubed end fraction
(−4)372
To simplify the expression 150⋅7^(-2)(-4)^(-3) with only positive exponents, we can apply the properties of integer exponents.
Firstly, we can rewrite 7^(-2) as 1/7^2, and (-4)^(-3) as 1/(-4)^3.
Now, the expression becomes:
150 * 1/7^2 * 1/(-4)^3
Simplifying further:
150 * 1/49 * 1/(-64)
Rearranging the terms:
150/49 * 1/(-64)
To get rid of the negative exponent, we move the negative sign to the numerator:
-150/49 * 1/64
Thus, the equivalent expression with only positive exponents is -150/49 * 1/64.
Firstly, we can rewrite 7^(-2) as 1/7^2, and (-4)^(-3) as 1/(-4)^3.
Now, the expression becomes:
150 * 1/7^2 * 1/(-4)^3
Simplifying further:
150 * 1/49 * 1/(-64)
Rearranging the terms:
150/49 * 1/(-64)
To get rid of the negative exponent, we move the negative sign to the numerator:
-150/49 * 1/64
Thus, the equivalent expression with only positive exponents is -150/49 * 1/64.
Apply All Exponent Rules Quick Check
4 of 54 of 5 Items
Question
Which of the following is the equivalent expression to (15−3 ⋅ 47)04−3 that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
164
Start Fraction 1 over 64 end fraction
604−3
Start Fraction 60 over 4 negative cubed end fraction
64
64
1⋅4−3
4 of 54 of 5 Items
Question
Which of the following is the equivalent expression to (15−3 ⋅ 47)04−3 that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
164
Start Fraction 1 over 64 end fraction
604−3
Start Fraction 60 over 4 negative cubed end fraction
64
64
1⋅4−3
To find the equivalent expression to (15^−3 ⋅ 4^7)^0^−3, let's break it down step by step:
Step 1: Simplify the exponents.
(15^−3 ⋅ 4^7)^0^−3 = (1/15^3 ⋅ 4^7)^0^−3
Step 2: Simplify the inner parentheses.
(1/15^3 ⋅ 4^7)^0^−3 = (1/15^3 ⋅ 16384)^0^−3
Step 3: Simplify the exponent within the parentheses.
(1/15^3 ⋅ 16384)^0^−3 = (1/15^3 ⋅ 16384)^0
Step 4: Any number raised to the power of 0 equals 1.
(1/15^3 ⋅ 16384)^0 = 1
Therefore, the correct equivalent expression is 1.
Step 1: Simplify the exponents.
(15^−3 ⋅ 4^7)^0^−3 = (1/15^3 ⋅ 4^7)^0^−3
Step 2: Simplify the inner parentheses.
(1/15^3 ⋅ 4^7)^0^−3 = (1/15^3 ⋅ 16384)^0^−3
Step 3: Simplify the exponent within the parentheses.
(1/15^3 ⋅ 16384)^0^−3 = (1/15^3 ⋅ 16384)^0
Step 4: Any number raised to the power of 0 equals 1.
(1/15^3 ⋅ 16384)^0 = 1
Therefore, the correct equivalent expression is 1.
Which property of exponents was used to generate the equivalent expression 3^14 from 3^5 3^−9?