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Simplify. Assume all variables are positive. $\newline$ $y^{\frac{1}{7}} \cdot y^{\frac{4}{7}}$ $\newline$ Write your answer in the form $A$ or $\frac{A}{B}$ , where $A$ and $B$ are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. $\newline$ ______

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Simplify expressions involving rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

y^{\frac{1}{7}} \cdot y^{\frac{4}{7}}

\newline

Write your answer in the form

A

or

\frac{A}{B}

, where

A

and

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

______

Identify Equation Property: Identify the equation and apply the property of exponents for multiplication, which states that when multiplying like bases, you add the exponents: $y^{a} \times y^{b} = y^{a+b}$ .
Add Exponents: Add the exponents $\frac{1}{7}$ and $\frac{4}{7}$ together: $\left(\frac{1}{7}\right) + \left(\frac{4}{7}\right) = \frac{5}{7}$ .
Write Simplified Expression: Write the simplified expression using the sum of the exponents: $y^{\frac{1}{7}} \times y^{\frac{4}{7}} = y^{\frac{5}{7}}$ .
Check Final Expression: Check that the final expression has a positive exponent and that there are no variables in common in the numerator and denominator, which is true since the expression is $y^{\frac{5}{7}}$ .

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