To apply the properties of integer exponents, we need to remember a few rules:
1) Any nonzero number raised to the power of 0 is equal to 1. (a^0 = 1)
2) To raise a number to a negative exponent, we can place it in the denominator and change the sign of the exponent. (a^(-b) = 1/a^b)
Let's simplify the given expression step by step:
15^0 X 7^−2 / (−4)^−3
Since any nonzero number raised to the power of 0 is equal to 1, 15^0 is 1:
1 X 7^−2 / (−4)^−3
Using the rule for negative exponents, we place 7^−2 in the denominator:
1 / 7^2 / (−4)^−3
Using the rule for negative exponents again, we place (−4)^−3 in the denominator:
1 / 7^2 X (−4)^3
This simplifies to:
1/49 X (-64)
Now, let's generate an expression with only positive exponents:
1/49 X (-64) = (-64)/49
Therefore, the equivalent expression with only positive exponents that has been generated by applying the Properties of Integer Exponents is, (-64)/49, which is not one of the given options.
Answer: None of the above.
Which of the following is an equivalent expression to 15^0 X 7^−2 / (−4)^−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?
A: 4^2/7^2
B: 7^2/(-4)^2
C: 1/7^2 X (-4)^-3
D: (-4)^3/7^2
5 answers
Thats not possible, try again because it has to be one of the answers
Apologies for the mistake earlier. Let's try again to find an equivalent expression with only positive exponents.
Starting with the given expression: 15^0 X 7^−2 / (−4)^−3
Using the property that any nonzero number raised to the power of 0 is equal to 1, we have:
1 X 7^−2 / (−4)^−3
Using the rule for negative exponents, we can write it as:
1 / 7^2 X (1 / (−4)^3)
Simplifying further, we have:
1 / 49 X (1 / (−64))
To make the exponents positive, we can move the negative sign from the base to the exponent:
1 / 49 X (1 / (1 / (64)))
Simplifying the reciprocal in the denominator, we get:
1 / 49 X 64
Now, let's simplify the expression:
1 / 49 X 64 = 64 / 49
Therefore, the equivalent expression with only positive exponents that has been generated by applying the Properties of Integer Exponents is 64/49.
Answer: None of the above.
Starting with the given expression: 15^0 X 7^−2 / (−4)^−3
Using the property that any nonzero number raised to the power of 0 is equal to 1, we have:
1 X 7^−2 / (−4)^−3
Using the rule for negative exponents, we can write it as:
1 / 7^2 X (1 / (−4)^3)
Simplifying further, we have:
1 / 49 X (1 / (−64))
To make the exponents positive, we can move the negative sign from the base to the exponent:
1 / 49 X (1 / (1 / (64)))
Simplifying the reciprocal in the denominator, we get:
1 / 49 X 64
Now, let's simplify the expression:
1 / 49 X 64 = 64 / 49
Therefore, the equivalent expression with only positive exponents that has been generated by applying the Properties of Integer Exponents is 64/49.
Answer: None of the above.
incorrect again, which answer is it?
Apologies for the confusion. Let's go through the steps again to find the correct equivalent expression.
Starting with the given expression: 15^0 X 7^−2 / (−4)^−3
Using the property that any nonzero number raised to the power of 0 is equal to 1, we have:
1 X 7^−2 / (−4)^−3
Using the rule for negative exponents, we can write it as:
1 / 7^2 X (1 / (−4)^3)
Simplifying further, we have:
1 / 49 X (1 / (−64))
To make the exponents positive, we can move the negative sign from the base to the exponent:
1 / 49 X (1 / (1 / (64)))
Simplifying the reciprocal in the denominator, we get:
1 / 49 X 64/1
Multiplying the fractions, we have:
64 / (49 * 1)
Simplifying the denominator, we get:
64 / 49
Therefore, the final equivalent expression with only positive exponents is 64/49.
Answer: D: (-4)^3/7^2
Starting with the given expression: 15^0 X 7^−2 / (−4)^−3
Using the property that any nonzero number raised to the power of 0 is equal to 1, we have:
1 X 7^−2 / (−4)^−3
Using the rule for negative exponents, we can write it as:
1 / 7^2 X (1 / (−4)^3)
Simplifying further, we have:
1 / 49 X (1 / (−64))
To make the exponents positive, we can move the negative sign from the base to the exponent:
1 / 49 X (1 / (1 / (64)))
Simplifying the reciprocal in the denominator, we get:
1 / 49 X 64/1
Multiplying the fractions, we have:
64 / (49 * 1)
Simplifying the denominator, we get:
64 / 49
Therefore, the final equivalent expression with only positive exponents is 64/49.
Answer: D: (-4)^3/7^2
4 answers