Which of the following is an equivalent expression to 14−79−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
Responses
1913 ⋅14−7
Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction
913147
Start Fraction 9 superscript 13 baseline over 14 superscript 7 baseline end fraction
14−7⋅913
14 superscript negative 7 baseline times 9 superscript 13 baseline
147913
Start Fraction 14 superscript 7 baseline over 9 superscript 13 baseline End Fraction
The correct answer is:
Start Fraction 9 superscript 13 baseline over 14 superscript 7 baseline end fraction
To find an equivalent expression with only positive exponents, we can apply the Property of Negative Integer Exponents, which states that any negative exponent can be rewritten as its positive reciprocal.
Given the expression 14−79−13, we can start by rewriting 14 as 14^1 (since any number to the power of 1 is itself):
14−7 = 14^1−7
Now, we can apply the Property of Negative Integer Exponents to the exponent -7:
14^1−7 = 14^1 ÷ 14^7
To simplify further, we can combine the bases with the same exponent:
14^1 ÷ 14^7 = 14^(1-7) = 14^-6
Finally, we can rewrite the negative exponent as its positive reciprocal:
14^-6 = 1 ÷ 14^6
Therefore, the equivalent expression with only positive exponents is 1 ÷ 14^6, which corresponds to the option "Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction."
To find an equivalent expression with only positive exponents, we can apply the Property of Negative Integer Exponents, which states that a negative exponent is equivalent to taking the reciprocal of the base raised to the positive exponent.
Given the expression 14 - 79 - 13, we need to rewrite it with positive exponents.
First, let's apply the Property of Negative Integer Exponents to the term 14 raised to the exponent -7. Taking the reciprocal of 14^-7 means putting it in the denominator with the exponent changed to positive 7:
14^-7 becomes 1 / 14^7
Now we have:
14 - 79 - 13 = 1 / 14^7
Next, let's analyze the answer choices.
- 1913 ⋅14^-7 : This is already in the form we obtained above, so it's a possibility.
- 1/9^13 * 14^-7: This combines two terms with different bases, so it's not equivalent to the original expression.
- 14^-7⋅913: This is the same as 1 / 14^7 * 9^13, which is not the same as the original expression.
- 14^7 / 9^13: This is the reciprocal of the expression we obtained above, so it's not equivalent to the original expression.
Out of the given choices, the equivalent expression with only positive exponents is:
1913 ⋅14^-7
So the correct answer is:
1913 ⋅14^-7