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).
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
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