apply the properties of integer exponents to generate equivalent expressions to 3^7 x 3^-9
with only positive exponents then solve the expression the answer has to a simplified fraction with no remaining exponents
I apologize for the incorrect response. Let's start again.
To generate equivalent expressions with only positive exponents for 3^7 x 3^-9, we can use the property of multiplying exponents with the same base, which states that a^m x a^n = a^(m+n).
So, applying this property, we have:
3^7 x 3^-9 = 3^(7 + (-9))
To simplify further, we can add the exponents:
3^(7 + (-9)) = 3^-2
Now, let's apply the property of a^(-n) = 1/a^n:
3^-2 = 1/3^2
Simplifying 1/3^2, we have:
1/3^2 = 1/9
Therefore, the equivalent expression to 3^7 x 3^-9 with only positive exponents is 1/9, which is already in simplified fraction form with no remaining exponents.
To generate equivalent expressions with only positive exponents, you can apply the property of integer exponents which states that a^(-n) is equal to 1/a^n.
So, applying this property to 3^-9, we can rewrite it as 1/(3^9).
Now, we can rewrite the expression 3^7 x 3^-9 using the equivalent expression.
3^7 x 3^-9 = 3^7 x (1/(3^9))
Next, we can apply the property of multiplying exponents with the same base, which states that a^m x a^n = a^(m+n).
Therefore, 3^7 x (1/(3^9)) = 3^(7 + 9)
Simplifying further,
3^(7 + 9) = 3^16
Now, to solve the expression into a simplified fraction with no remaining exponents, we can express 3^16 as a fraction.
Since the base is 3, we can write it as 3^16/1.
Thus, the simplified fraction form of 3^7 x 3^-9 is 3^16/1.
wrong
To generate equivalent expressions with only positive exponents, we can use the properties of integer exponents:
1. Product Rule: a^m * a^n = a^(m + n)
2. Quotient Rule: a^m / a^n = a^(m - n)
3. Zero Exponent Rule: a^0 = 1
Let's apply these rules step-by-step to 3^7 * 3^(-9):
Step 1: Use the Product Rule to combine the exponents of the same base, 3.
3^7 * 3^(-9) = 3^(7 + (-9))
Step 2: Simplify the exponent by adding (-9) to 7.
3^(-2)
Now, we have an equivalent expression with only a positive exponent, 3^(-2).
To solve this expression and obtain a simplified fraction, we can use the definition of a negative exponent, which states that a^(-n) = 1 / a^n.
So, 3^(-2) = 1 / 3^2
Squaring 3, we get:
3^2 = 9
Therefore, the simplified fraction for the expression 3^7 * 3^(-9) is 1/9.
To apply the properties of integer exponents to generate equivalent expressions for 3^7 x 3^-9, we can use the rule that states:
For any positive integer a and integers m and n, where m ≥ n, a^m/a^n = a^(m-n).
Step 1: Rewrite 3^-9 as 1/3^9.
We can apply this rule by subtracting the exponents:
3^7 x 1/3^9
Step 2: Combine the product of 3^7 and 1/3^9.
Using the rule that a^m x a^n = a^(m+n), we can combine the terms:
3^7 x 1/3^9 = 3^(7+(-9)) = 3^-2.
Step 3: Simplify the expression with no negative exponent.
Since we want to express the answer with only positive exponents, we can rewrite 3^-2 as 1/3^2.
3^-2 = 1/3^2.
Step 4: Evaluate the expression.
Substituting the value into the expression:
1/3^2 = 1/9.
Therefore, the result of 3^7 x 3^-9, with only positive exponents and as a simplified fraction, is 1/9.