Question

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.

Answer 1

To generate equivalent expressions with only positive exponents, we can use the product rule of exponents and the power of a power rule. The simplified fraction with no remaining exponents is 60466176.

Step-by-step explanation:

To apply the properties of integer exponents to generate equivalent expressions with only positive exponents, we can use the following steps:

1. First, apply the product rule of exponents: 143⋅27 = (14⋅3)⋅(2⋅3⋅3) = 2⋅3⋅3⋅3⋅2⋅3⋅3 = 2²⋅3⁶.
2. Next, apply the power of a power rule: (2²⋅3⁶)⁰³⁴ = 2²⁰⋅3²⁰.

The equivalent expression is 2²⁰⋅3²⁰. Now, to solve the expression:

2²⁰⋅3²⁰ = (2⋅3)²⁰ = 6²⁰ = 60466176.

Therefore, the simplified fraction with no remaining exponents is 60466176.