Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7⋅3^−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
3^7⋅3^−9=
To generate equivalent expressions with only positive exponents, we can use the property of integer exponents that states:
a^m ⋅ a^n = a^(m+n)
Applying this property to the given expression:
3^7 ⋅ 3^(-9)
We can now add the exponents:
7 + (-9) = -2
The equivalent expression with only positive exponents is therefore:
3^(-2)
To solve this expression, we can rewrite it as a fraction using the property that negative exponents indicate the reciprocal of the positive exponent:
3^(-2) = 1/3^2 = 1/9
Therefore, the simplified fraction with no remaining exponents is 1/9.
Apply the Properties of Integer Exponents to generate equivalent expressions to 222−4
with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
222−4=
To generate an equivalent expression with only positive exponents for 3^7⋅3^−9, we can use the product rule, which states that when multiplying two numbers with the same base, we add their exponents.
So, 3^7⋅3^−9 can be rearranged as 3^(7 + -9).
To simplify this further, we can use the property that any number with an exponent of 0 is equal to 1. Therefore, 3^0 = 1.
Therefore, 3^(7 + -9) can be written as 3^(-2).
To eliminate the negative exponent, we can apply the property that a number raised to a negative exponent can be written as the reciprocal of the number raised to the absolute value of the exponent. In this case, 3^(-2) can be written as 1/(3^2).
Simplifying further, 3^2 = 9. Therefore, the final expression is:
1/9.
So, 3^7⋅3^−9 is equal to 1/9.
To generate an equivalent expression to 3^7⋅3^−9 with only positive exponents, we can use the property of integer exponents which states that when multiplying powers with the same base, we can add their exponents.
So, for 3^7⋅3^−9, we can add the exponents: 7 + (-9) = -2.
Therefore, the equivalent expression with only positive exponents is 3^(-2).
Now, to solve the expression 3^(-2), we can rewrite it as a fraction by using the definition of negative exponents: a^(-n) = 1/a^n.
In this case, we have 3^(-2), which can be rewritten as 1/3^2.
Simplifying 1/3^2, we have 1/9.
Hence, the answer to the expression 3^7⋅3^−9 is 1/9, which is a simplified fraction with no remaining exponents.