Apply the Property of Negative Integer Exponents to generate an expression equivalent to with positive exponents only.(1 point) 3^−17/8^−14
Using the property of negative integer exponents, we can rewrite the expression as:
(8^14/3^17)
This expression has positive exponents only.
so i swithc them around
Apologies for the confusion in my initial response. When applying the property of negative integer exponents, the correct approach is to switch the base with its reciprocal. Thus, we can rewrite the expression as:
(8^14/3^17) = (1/3^17)/(1/8^14) = (8^14/3^17)
i know but do i just swich them and i get the answer
Apologies for the confusion again. If you switch the base and its reciprocal, you need to simplify further. Here's the correct process:
Starting with the expression (3^(-17))/(8^(-14)), applying the property of negative integer exponents, we can rewrite it as:
(1/(3^17))/(1/(8^14))
Next, we can simplify this further by multiplying the numerator and denominator by the reciprocal of the second fraction:
(1/(3^17))*(8^14/1)
Now we have:
(8^14)/(3^17)
This expression has positive exponents only.
Apply the Properties of Integer Exponents to generate equivalent expressions to with only positive exponents, then solve the expression. Provide the answer as an improper fraction.(1 point) heres to the problem (7^−3)^7x7^20/6^−2
To apply the properties of integer exponents and simplify the expression (7^(-3))^7 * 7^20 / 6^(-2), we can follow these steps:
Step 1: Simplify the expression (7^(-3))^7 using the property of a power raised to a power: (a^m)^n = a^(m*n).
(7^(-3))^7 = 7^(-3 * 7) = 7^(-21)
Step 2: Rewrite the expression with positive exponents only.
7^(-21) * 7^20 / 6^(-2) = 7^(-21 + 20) / 6^(-2)
Step 3: Simplify further using the property of a quotient with the same base: a^m / a^n = a^(m - n).
7^(-21 + 20) / 6^(-2) = 7^(-1) / 6^(-2) = 7^(-1 - (-2)) = 7^1 / 6^2
Step 4: Evaluate the expression.
7^1 / 6^2 = 7 / 36
Therefore, the expression (7^(-3))^7 * 7^20 / 6^(-2) simplifies to the improper fraction 7/36.
it has to be improper
Apologies for the oversight. To express the result as an improper fraction, we can write 7/36 as 0 remainder 7/36.
To apply the property of negative integer exponents and generate an expression with positive exponents, we can use the following rule:
For any non-zero number a and any integer n, \(a^{-n} = \frac{1}{a^n}\).
Let's apply this rule to the given expression \(3^{-17}/8^{-14}\):
1. Rewrite \(3^{-17}\) using the property of negative exponents:
\(3^{-17} = \frac{1}{3^{17}}\)
2. Rewrite \(8^{-14}\) using the property of negative exponents:
\(8^{-14} = \frac{1}{8^{14}}\)
Now, substituting these values back into the expression:
\(\frac{1}{3^{17}}/\frac{1}{8^{14}}\)
When you divide fractions, you can multiply the numerator by the reciprocal of the denominator. So, multiplying the numerator by \(8^{14}\) (reciprocal of \(1/8^{14}\)) we get:
\(\frac{1}{3^{17}} \times 8^{14}\)
Finally, we have an equivalent expression with positive exponents only:
\(\frac{8^{14}}{3^{17}}\)