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Chapter 5: Problem 10

Simplify $$ \frac{y^{6} y^{-3} y^{0.5}}{y^{-2} y^{7}} $$

Short Answer

Expert verified
Answer: The simplified form of the expression is \(y^{-1.5}\).

Step by step solution

01

Combine the numerators' exponents

Add the exponents of y in the numerator: $$ y^{6} y^{-3} y^{0.5} = y^{6-3+0.5} = y^{3.5} $$
02

Combine the denominators' exponents

Add the exponents of y in the denominator: $$ y^{-2} y^{7} = y^{-2+7} = y^5 $$
03

Simplify the fraction

Divide the entire expression by subtracting the exponents: $$ \frac{y^{3.5}}{y^5} = y^{3.5-5} = y^{-1.5} $$ So the simplified expression is \(y^{-1.5}\).

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