What is the equivalent expression of 14 with the power of 7 over 9 with the power of 13 - both with only positive equivalents generated by applying the property of negative integer
To find the positive equivalent of (-14)¹³/⁹, we can first simplify the exponent and then remove the negative sign.
The exponent 13 is odd, so (-14)¹³ would remain negative.
To simplify the exponent 13/9, we can write it as (13/9) * 1. Since any number raised to the power of 1 remains the same, we can remove the exponent temporarily, which gives us (-14) * 1.
Therefore, the positive equivalent of (-14)¹³/⁹ is just 14.
To find the equivalent expression of 14 with the power of 7 over 9 with the power of 13 using only positive equivalents, we need to apply the property of negative exponents.
First, let's rewrite the expression without negative exponents:
14^7 / 9^13
Now, we'll apply the property of negative exponents, which states that a^(-b) is equal to 1 / a^b:
1 / (14^7 / 9^13)
Next, let's simplify the expression:
1 / [(14^7) / (9^13)]
To simplify further, we can multiply the numerator by the reciprocal of the denominator:
(9^13) / (14^7)
Therefore, the equivalent expression of 14 with the power of 7 over 9 with the power of 13, using only positive equivalents generated by applying the property of negative exponents, is (9^13) / (14^7).
To find the equivalent expression with positive exponents, we can use the property of negative exponents which states that a number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.
Given the expression: 14^(7/9)^(13)
1. First, we deal with the denominator exponent (9). To remove the denominator, we can raise the entire expression to the power of 9 to get rid of the fractional exponent.
(14^(7/9)^(13))^9
2. Now, we can apply the property of negative exponents to make the exponent positive. We take the reciprocal of the base raised to the positive exponent.
[(14^(7/9)^(13))^9] = [(1 / 14^(-7/9))^9]
Now, the expression is in a form where both the base and the exponent are positive.