1. Which of the following is developed to be equivalent to 1/8^5
8^-5
8 1/5
5^-8
8^5
2. Which of the following is equivalent to 6^-2?
36
1/2^6
1/6^-2
1/36
3. Which of the following is an equivalent expression to 13^-5 x 13^-11 with only positive exponents, generated by applying the properties of exponents?
1/13^16
1/26^16
1/26^6
1/13^6
4.Which of the following is an equivalent expression to 14^-7/9^-13 with only positive exponents, generated by applying the properties of exponents?
14^7/9^13
9^13/14^7
14^-7 x 9^13
1/9^13 x 14^-7
5. Which of the following is an equivalent expression to 7^3/25^-4 with only positive exponents, generated by applying the properties of exponents?
25^4/7^-3
25^4/7^3
7^3/25^4
7^3 x 25^4
1. To find the expression equivalent to 1/8^5, we need to apply the rule of negative exponents. The rule states that any number raised to a negative exponent can be expressed as the reciprocal of the number raised to the positive exponent. So, 1/8^5 can be written as 8^-5.
2. To find the expression equivalent to 6^-2, we need to apply the rule of negative exponents. Similar to the previous question, 6^-2 can be written as the reciprocal of 6^2, which is 1/6^2.
3. To simplify the expression 13^-5 x 13^-11, we can add the exponents of 13. The rule states that when we multiply two numbers with the same base, we can add their exponents. In this case, 13^-5 x 13^-11 can be simplified to 13^(-5 + -11), which equals 13^-16. To express this with only positive exponents, we take the reciprocal of 13^-16, giving us 1/13^16.
4. To simplify the expression 14^-7/9^-13, we can apply the rule of negative exponents again. The rule states that when we divide two numbers with the same base, we can subtract their exponents. So, 14^-7/9^-13 can be written as 14^-7 x 9^13. This expression has only positive exponents.
5. To simplify the expression 7^3/25^-4, we can apply the rule of negative exponents yet again. The rule states that when we have a negative exponent in the denominator, we can move it to the numerator and change its sign. So, 7^3/25^-4 can be written as 7^3 x 25^4. This expression has only positive exponents.
1. 8^-5
2. 1/6^-2
3. 1/13^16
4. 14^7/9^13
5. 7^3 x 25^4