Apply the properties of integer exponents 3*7×3*-9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents
To apply the properties of integer exponents and eliminate the negative exponents, we can use the following rules for multiplication and division of exponents:
1. When multiplying two numbers with the same base but different exponents, we add the exponents.
2. When dividing two numbers with the same base but different exponents, we subtract the exponent of the divisor from the exponent of the dividend.
Let's apply these rules to the expression 3*7×3*-9:
First, we can rearrange the expression using the associative property of multiplication:
3 * 3 * 7 * (3^(-9))
Now, let's multiply the numbers and combine the exponents:
3 * 3 = 3^2
3^2 * 7 = 3^2 * 7^1
3^2 * 7^1 * 3^(-9)
Next, we can combine the exponents using the rule for multiplication:
3^2 * 7^1 * 3^(-9) = 3^(2 + (-9)) * 7^1
Simplifying the exponent:
3^(2 + (-9)) = 3^(-7)
Therefore, the expression 3*7×3*-9 with positive exponents is equivalent to 3^(-7) * 7^1.
To further simplify the expression, we combine the bases and convert them to a fraction format:
3^(-7) * 7^1 = 1/(3^7) * 7/1
Combining the fractions:
1/(3^7) * 7/1 = 7/(3^7)
Therefore, the simplified fraction with no remaining exponents is 7/(3^7).
To simplify the expression 3*7×3*-9 with positive exponents, we can apply the properties of integer exponents.
The property states that for any nonzero number 'a' and integers 'm' and 'n', we have:
a^m * a^n = a^(m + n)
Let's apply this property step by step:
Step 1: Simplify the exponents by adding them:
3 * 7 * 3^-9 = 3^(1+(-9))
Step 2: Simplify the exponent:
3^(1+(-9)) = 3^-8
Step 3: According to the property of integer exponents, any number raised to the power of -n can be rewritten as 1 divided by that number raised to the power of n:
3^-8 = 1 / 3^8
Therefore, the simplified expression of 3*7×3*-9 with positive exponents is 1 / 3^8.
Note: The expression cannot be further simplified into a fraction without any remaining exponents, as 3^8 is already in its simplest form.
To apply the properties of integer exponents, we need to simplify the expression by using the rules of multiplication and division of exponents.
Step 1: Apply the rule of multiplication:
When multiplying two numbers with the same base, we add their exponents.
3 * 7 = 3^(1+1) = 3^2
Step 2: Apply the rule of division:
When dividing two numbers with the same base, we subtract the exponent of the denominator from the exponent of the numerator.
3^2 / 3^9 = 3^(2-9) = 3^-7
Step 3: Simplify the expression:
To convert a negative exponent to a positive exponent, we can take the reciprocal of the base with the positive exponent.
3^-7 = 1 / 3^7
Therefore, the simplified expression becomes:
1 / 3^7
This cannot be simplified further since there are no common factors between 1 and 3^7. So the answer is 1/3^7, which is a simplified fraction with no remaining exponents.