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

Answer 1

To apply the Properties of Integer Exponents, let's break down the expression step by step:

First, let's rewrite the expression with positive exponents:

(143⋅27^(-7))^034

Now, let's apply the Power of a Product property:

(143^034)(27^(-7*034))

Simplify -7*034:

(143^034)(27^(-238))

Now, let's apply the Power of a Power property:

(143^034)(27^(-238))

Now, let's solve the expression:

Using a calculator, we find that 143 raised to the power of 34 is:

143^034 ≈ 2.8 x 10^62 (rounded to one decimal place)

Similarly, using a calculator, we find that 27 raised to the power of -238 is approximately:

27^(-238) ≈ 5.0356 x 10^(-391) (rounded to four decimal places)

So, the simplified fraction is:

2.8 x 10^62 / 5.0356 x 10^(-391)

To simplify, we divide the coefficients and subtract the exponents:

2.7941 x 10^(62+391) = 2.7941 x 10^453

Therefore, the answer is 2.7941 x 10^453, which is a simplified fraction with no remaining exponents.