Which of the following is an equivalent expression of 13 - power of 5.13 - power of 11 with only positive exponents generated by applying the properties of exponents 126 powers 113th power of 6 113th power of 16126 power system
The equivalent expression of \(13^{5} \cdot 13^{11}\) with only positive exponents would be \(13^{5+11} = 13^{16}\).
To simplify the expression 13 - power of 5.13 - power of 11 and generate an equivalent expression with only positive exponents using the properties of exponents, we can use the rule that states x^a / x^b = x^(a-b). Let's break it down step-by-step:
1. Start with the expression 13 - power of 5.13 - power of 11.
2. Apply the property of exponents by subtracting the exponents of the same base, which is 13. So we have 5 - 11 = -6.
3. Rewrite the expression as 13^-6.
4. To eliminate negative exponents, we can use the rule that states x^-n = 1 / x^n. In this case, x is 13 and n is 6.
5. Substitute the values into the rule and rewrite the expression: 1 / 13^6.
Therefore, an equivalent expression with only positive exponents would be 1 / 13^6.
To find an equivalent expression of 13 raised to the 5th power minus 13 raised to the 11th power with only positive exponents, you can use the properties of exponents. Let's break it down step by step:
Step 1: Rewrite the original expression using the properties of exponents.
13^5 - 13^11
Step 2: Simplify the expression by factoring out the common factor of 13^5.
13^5 * (1 - 13^6)
Step 3: Further simplify the expression by applying the property of exponents, which states that a^m * a^n = a^(m+n).
13^5 * (1 - 13^6)
Step 4: Finally, the equivalent expression with only positive exponents is:
126 * (1 - 16126)
In summary, the equivalent expression of 13^5 - 13^11 with only positive exponents is 126 * (1 - 16126).