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.(1 point)
(143⋅27−7)034=

Answer 1

Apply the Properties of Integer Exponents to generate equivalent expressions to (43 ⋅ 7−2)−579 ⋅ 4−13 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(43 ⋅ 7−2)−579 ⋅ 4−13 =

Answer 2

To apply the properties of integer exponents, we can break down the given expression step by step:

1. Expand the expression inside the parentheses: (143⋅27−7)034 = (3819 - 7)034.

2. Simplify the expression within the parentheses: (3819 - 7) = 3812.

3. Raise 3812 to the power of 034: 3812^34.

Since the original expression only contains positive exponents, we do not need to apply any additional properties.

Now, to solve the expression 3812^34, we need to find a way to simplify it without calculating the actual value. One way to do this is by expressing it as a fraction with no remaining exponents.

Let's represent the simplified expression as a fraction:

3812^34 / 1

Now, let's find a way to reduce the exponents. We know that any number raised to the power of 1 is the number itself, so we can rewrite it as:

(3812^17)^2 / 1

Next, we can rewrite this fraction using the property of multiplying exponents:

3812^(17*2) / 1

Now, we can simplify the exponent:

3812^34 / 1

Therefore, the simplified fraction is 3812/1, which can be written as the whole number 3812.