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
12616
Start Fraction 1 over 26 superscript 16 baseline end fraction
1136
Start Fraction 1 over 13 Superscript 6 baseline End Fraction
1266
Start Fraction 1 over 26 superscript 6 baseline end fraction
11316
The equivalent expression to 13−5 ⋅13−11 with only positive exponents is:
Start Fraction 1 over 13 Superscript 6 baseline End Fraction, which is equal to 1136.
To simplify the expression 13−5 ⋅13−11 and rewrite it with positive exponents, we can use the property of exponents which states that a negative exponent is equivalent to the reciprocal of the positive exponent.
First, let's rewrite the expression using the reciprocal of the negative exponents:
13−5 ⋅ 13−11 = 1/135 ⋅ 1/1311
Next, let's simplify the expression by multiplying the fractions:
1/135 ⋅ 1/1311 = 1/13511
Therefore, the equivalent expression with only positive exponents is:
Start Fraction 1 over 13511 End Fraction