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Apply the Properties of Integer Exponents to generate equivalent expressions to (4*3 ⋅ 7*−2)*−5 7*9 ⋅ 4−*13 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
To simplify the given expression and convert it to an equivalent expression with only positive exponents, we can apply the properties of integer exponents. Let's break it down step by step:
Step 1: Apply the property of negative exponents:
1/(4^3 * 7^(-2)) * 7^9 * 4^(-13)
Step 2: Multiply the coefficients:
(1/(4^3 * 7^(-2))) * (7^9 * 4^(-13))
Step 3: Apply the property of multiplying exponents with the same base:
1/(4^(3+(-13)) * 7^(-2+9))
Step 4: Simplify the exponents:
1/(4^(-10) * 7^7)
Step 5: Apply the property of negative exponents:
7^7 / 4^10
Therefore, the simplified fraction expression with positive exponents is:
7^7 / 4^10
To solve this expression further, we can calculate the values of 7^7 and 4^10:
7^7 ≈ 823,543
4^10 = 1,048,576
So, the solution to the expression is:
823,543 / 1,048,576
This fraction can be further simplified if needed.
simplify it please
Certainly! Let's simplify the fraction 823,543 / 1,048,576:
First, we can simplify the numerator and denominator by finding the greatest common divisor (GCD) of the two numbers. The GCD of 823,543 and 1,048,576 is 1.
Dividing both the numerator and denominator by 1, we get:
823,543 / 1,048,576 = 823,543 / 1,048,576
Since the GCD is 1, the fraction is already in its simplified form.