Apply the Properties of integer exponents to generate an equivalent expression to 3^7x3^(-9) with only positive exponents, then solve the expression. Simplified.
To generate an equivalent expression with only positive exponents, we can use the property of integer exponents that states:
a^m / a^n = a^(m-n)
In this case, we have 3^7 * 3^(-9). We can combine these two expressions using the above property:
3^7 * 3^(-9) = 3^(7-9) = 3^(-2)
Now, to solve the expression, we need to calculate 3^(-2). Using the property that a^(-n) = 1/a^n, we have:
3^(-2) = 1/3^2 = 1/9
Therefore, the simplified expression is 1/9.
To generate an equivalent expression with only positive exponents, we can use the property of integer exponents that states: a^m * a^n = a^(m + n).
Step 1: Apply the property of integer exponents to the expression 3^7 * 3^(-9):
3^7 * 3^(-9) = 3^(7 + (-9))
Step 2: Simplify the exponent:
3^(-2)
To solve this expression, we can use the property of negative exponents, which states: a^(-n) = 1/a^n.
Step 3: Apply the property of negative exponents to the expression 3^(-2):
3^(-2) = 1 / 3^2
Step 4: Simplify the expression further:
1 / 3^2 = 1 / 9
Therefore, the simplified equivalent expression to 3^7 * 3^(-9) with only positive exponents is 1/9.
To generate an equivalent expression with only positive exponents, we can use the property of exponentiation that states:
a^m * a^n = a^(m+n)
Using this property, let's simplify the given expression:
3^7 * 3^(-9)
Applying the exponent property, we can combine the exponents:
3^(7 + (-9))
Since adding a negative exponent is the same as subtracting its absolute value, we have:
3^(7 - 9)
Simplifying further, we get:
3^(-2)
Since 3^(-2) is in the form of a negative exponent, we'll rewrite it using the reciprocal property of exponents:
3^(-2) = 1 / (3^2)
Now we can calculate the value of the expression:
3^(-2) = 1 / (3^2) = 1 / 9
Therefore, the simplified expression of 3^7 * 3^(-9) is 1/9.