Which of the following is an equivalent expression written in exponential form to 5^9×5^-13 with only positive exponents that has been generated by applying the properties of exponents
1/5^4
5^9/5^-13
5^4
1/625
The equivalent expression written in exponential form with only positive exponents is 1/625.
Simplify using exponent rules: 7^4×7×7^13×7^-20
28^-2
1/7^2
1/7^3
1/7^-2
To simplify the expression 7^4 × 7 × 7^13 × 7^-20 using exponent rules, we can add the exponents for the same base and multiply the coefficients:
7^4 × 7 × 7^13 × 7^-20 = 7^(4 + 1 + 13 - 20) = 7^(-2)
Therefore, the simplified expression is 1/7^2
Fully simplify using exponent rules: (5^8/5^6)^2
1^4
5^2
25^4
5^4
To simplify the expression (5^8/5^6)^2 using exponent rules, we need to apply two rules:
Rule 1: When dividing two numbers with the same base, we subtract the exponents.
Rule 2: When raising a power to another power, we multiply the exponents.
Applying these rules, we can simplify the expression as follows:
(5^8/5^6)^2 = 5^(8-6)^2 = 5^2^2
Now, we can apply the second rule:
5^2^2 = 5^(2*2) = 5^4
Therefore, the fully simplified expression is 5^4.
Simplify using the exponent rules: (answer can only have positive exponents) (x^3)(×^-6)
x7
1/x^28
1/x13
x8
To simplify (x^3)(×^-6), we can apply the exponent rules as follows:
Multiply the coefficients: 1 * x^3 = x^3
Add the exponents since the bases are the same: x^3 * x^-6 = x^(3 + (-6)) = x^(-3)
To convert the expression to have positive exponents, we can rewrite it as 1/x^3.
Therefore, the simplified expression is 1/x^3.