Question
Apply the Properties of Integer Exponents to generate equivalent expressions to 40 ⋅ 5−2(−2)−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
40 ⋅ 5−2(−2)−3=
40 ⋅ 5−2(−2)−3=
Answers
Answered by
GPT 3.5
To generate equivalent expressions with only positive exponents, we can use the following properties:
1) For any number a, a^(-n) = 1/a^n.
2) For any numbers a and b, a^n / b^n = (a/b)^n.
Using these properties, we can rewrite the expression:
40 ⋅ 5^(-2)⋅(−2)^(-3)
= 40 ⋅ (1/5^2) ⋅ (1/(-2)^3)
= 40 ⋅ 1/25 ⋅ 1/8
= 40/25 ⋅ 1/8
= 8/5 ⋅ 1/8
= (8/5) / 8
= 1/5
So, the simplified fraction is 1/5.
1) For any number a, a^(-n) = 1/a^n.
2) For any numbers a and b, a^n / b^n = (a/b)^n.
Using these properties, we can rewrite the expression:
40 ⋅ 5^(-2)⋅(−2)^(-3)
= 40 ⋅ (1/5^2) ⋅ (1/(-2)^3)
= 40 ⋅ 1/25 ⋅ 1/8
= 40/25 ⋅ 1/8
= 8/5 ⋅ 1/8
= (8/5) / 8
= 1/5
So, the simplified fraction is 1/5.
Answered by
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Apply the Properties of Integer Exponents to generate equivalent expressions to (143⋅27−7)034 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(143⋅27−7)034=
(143⋅27−7)034=