Question
which of the following is an equivalent expression to 15^0 x 7^-2/(-4)^-3 with only positive exponents that have been generated by applying the Properties of Integer Exponents?
a. 4^3/7^2
b. 1/7^2 x (-4(^-3
c. 7^2/(-4)^3
d. (-4)^3/7^2
a. 4^3/7^2
b. 1/7^2 x (-4(^-3
c. 7^2/(-4)^3
d. (-4)^3/7^2
Answers
Answered by
ee
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Answered by
GPT 3.5
To simplify the expression 15^0 x 7^-2/(-4)^-3 and convert all exponents to positive, you can use the Properties of Integer Exponents. Recall that any number raised to the power of 0 is equal to 1.
First, apply the property that any number raised to the power of 0 is 1. So, 15^0 becomes 1.
Next, apply the property of negative exponents. Any number raised to a negative exponent can be rewritten by taking the reciprocal of the base and changing the sign of the exponent. Therefore, 7^-2 becomes 1/7^2, and (-4)^-3 becomes 1/(-4)^3.
Now, the expression becomes: 1 x 1/7^2 / 1/(-4)^3.
To simplify further, multiply by the reciprocal of the denominator: 1 x 1/7^2 x (-4)^3.
So, the equivalent expression with only positive exponents generated by applying the Properties of Integer Exponents is:
d. (-4)^3/7^2.
First, apply the property that any number raised to the power of 0 is 1. So, 15^0 becomes 1.
Next, apply the property of negative exponents. Any number raised to a negative exponent can be rewritten by taking the reciprocal of the base and changing the sign of the exponent. Therefore, 7^-2 becomes 1/7^2, and (-4)^-3 becomes 1/(-4)^3.
Now, the expression becomes: 1 x 1/7^2 / 1/(-4)^3.
To simplify further, multiply by the reciprocal of the denominator: 1 x 1/7^2 x (-4)^3.
So, the equivalent expression with only positive exponents generated by applying the Properties of Integer Exponents is:
d. (-4)^3/7^2.
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