Negative Integer Exponents Practice
Math 8 Q1 (Pre-Algebra) / Exponent Rules
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^−3 ⋅ 7^−5 with positive exponents only.(1 point)
To generate an expression equivalent to 7^−3 ⋅ 7^−5 with positive exponents only, we can apply the Property of Negative Integer Exponents, which states that a^−n = 1/a^n.
Therefore, 7^−3 ⋅ 7^−5 can be rewritten as 1/7^3 ⋅ 1/7^5.
To simplify this expression, we can use the product of powers property, which states that (a^n)(a^m) = a^(n+m).
So, 1/7^3 ⋅ 1/7^5 can be simplified to 1/7^(3+5).
Therefore, the expression equivalent to 7^−3 ⋅ 7^−5 with positive exponents only is 1/7^8.
To generate an expression equivalent to 7^−3 ⋅ 7^−5 with positive exponents only, we can use the property of negative integer exponents, which states that a^(-n) = 1/a^n.
Therefore, applying this property to each exponent, we have:
7^-3 ⋅ 7^-5 = 1/7^3 ⋅ 1/7^5
To simplify this expression, we can combine the two fractions using the rule a/b ⋅ c/d = (a⋅c)/(b⋅d):
1/7^3 ⋅ 1/7^5 = (1⋅1)/(7^3⋅7^5)
Since the base is the same (which is 7), we can combine the exponents by adding them:
= 1/7^(3+5)
Simplifying further:
= 1/7^8
Therefore, the expression equivalent to 7^-3 ⋅ 7^-5 with positive exponents only is 1/7^8.