Which of the following is an equivalent expression to 13−5 ⋅13−11 with only positive exponents, generated by applying the properties of exponents?(1 point)
Responses
11316
Start Fraction 1 over 13 superscript 16 baseline end fraction
1266
Start Fraction 1 over 26 superscript 6 baseline end fraction
1136
Start Fraction 1 over 13 Superscript 6 baseline End Fraction
12616
The equivalent expression with only positive exponents is:
Start Fraction 1 over 13 Superscript 6 baseline End Fraction
To simplify the expression 13−5 ⋅13−11 and express it with positive exponents, we can apply the properties of exponents.
The property we can use is x^a ⋅ x^b = x^(a+b).
In this case, we have 13^(-5) ⋅ 13^(-11).
Applying the property, we add the exponents: -5 + (-11) = -16.
So the equivalent expression with only positive exponents is:
Start Fraction 1 over 13 Superscript 16 Baseline End Fraction
To find the equivalent expression with positive exponents, we need to apply the properties of exponents. Recall the property that states when dividing two numbers with the same base, you subtract the exponents.
The given expression is 13 − 5 · 13 − 11. To simplify this, we first perform the multiplication: 5 · 13 = 65. Now we have 13 - 65 − 11.
Next, we apply the division property by subtracting the exponents: 13 - 65 - 11 = 13 - 76.
Finally, to write this expression with positive exponents, we can change the negative exponent to a positive exponent by taking the reciprocal of the base. In this case, we have 13 - 76 which simplifies to 1/13^76.
So, the equivalent expression with positive exponents is Start Fraction 1 over 13 superscript 76 baseline end fraction.