Q. Fully simplify using only positive exponents.16x8y824x3y5Answer:
Factor and Simplify: Write down the expression and factor both the numerator and the denominator.(24x3y5)/(16x8y8) can be factored as (8⋅3⋅x3⋅y5)/(8⋅2⋅x8⋅y8).
Simplify Coefficients: Simplify the coefficients by dividing 24 by 16. 1624 simplifies to 23 since both 24 and 16 are divisible by 8.
Apply Quotient Rule: Apply the quotient rule for exponents to simplify x3/x8 and y5/y8. x3/x8 simplifies to x−5 and y5/y8 simplifies to y−3, but we want only positive exponents.
Convert Negative Exponents: Convert negative exponents to positive exponents. x−5 becomes x51 and y−3 becomes y31.
Combine Coefficients and Exponents: Combine the simplified coefficients and the positive exponents. The expression now reads (23)×(x51)×(y31).
Write Final Expression: Write the final simplified expression.The fully simplified expression using only positive exponents is (23)×(x51×y31) or (23)×(x5y31).
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