Apply All Exponent Rules Practice
Math 8 Q1 (Pre-Algebra) / Exponent Rules
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.(1 point)
3^7⋅3^−9=___
I have no idea how long ago this was but if you still need the answers:
Question 1: 1/9
(Use the product rule of exponents to make 3^7 x 3^-9 into 3^-2 {7 + -9 = -2} which is 1/3^2 which is also 1/9)
Question 2: 64
(Use the quotient rule of exponents to make 2^2 / 2^-4 into 2^6 {2 - -4 = 6}, which solved is 64)
Question 3: -8/25
Question 4: 1/81
(Use the Zero power rule of exponents to make the numerator 1, then solve for 3^4, which is 81)
Question 5:
7/16
To apply the properties of integer exponents, we can use the rule that states:
a^m ⋅ a^n = a^(m+n)
Using this rule, we can rewrite the expression 3^7 ⋅ 3^−9 as:
3^(7+(-9))
Simplifying the exponent, we get:
3^(-2)
Since the exponent is negative, we can rewrite it as 1 over the positive exponent:
1/3^2
Simplifying further, we get:
1/9
Therefore, 3^7 ⋅ 3^−9 is equivalent to 1/9.
long division is correct ty
x anonymous
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)
Using this property, we can rewrite the expression 3^7 ⋅ 3^(-9) as:
3^(7+(-9))
Simplifying the exponent, we have:
3^(-2)
To solve the expression, we need to convert the negative exponent to a positive exponent. The Property of Integer Exponents states:
a^(-n) = 1 / a^n
Applying this property, we have:
3^(-2) = 1 / 3^2
Simplifying further, we have:
1 / 9
Therefore, the simplified fraction with no remaining exponents is 1/9.
To solve this problem, we need to apply the properties of integer exponents. The property we will use here is the product of powers property, which states that when multiplying exponential expressions with the same base, we can add their exponents.
The given expression is:
3^7 ⋅ 3^(-9)
To generate an equivalent expression with only positive exponents, we can rewrite 3^(-9) as 1/3^9.
Now we have:
3^7 ⋅ 1/3^9
Applying the product of powers property, we add the exponents:
3^(7-9), which simplifies to 3^(-2).
To solve the expression, we need to write 3^(-2) as a fraction with no remaining exponents. To convert a negative exponent to a positive exponent, we can write it as the reciprocal of the base raised to the positive exponent. So we have:
3^(-2) = 1 / 3^2
Simplifying 3^2, we get 9.
Therefore, 3^7 ⋅ 3^(-9) is equivalent to 1/9.