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Fully simplify using only positive exponents. (25xy^7)/(25xy^4)

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Fully simplify using only positive exponents.
(25xy^7)/(25xy^4)

Fully simplify using only positive exponents. (25xy^7)/(25xy^4)

Solução

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FernandoProfissional · Tutor por 6 anos

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To simplify the expression $\frac{25xy^7}{25xy^4}$, we can follow these steps:<br /><br />1. Cancel out the common factors in the numerator and denominator.<br />2. Simplify the remaining expression.<br /><br />Step 1: Cancel out the common factors<br />In the numerator and denominator, we have the common factors of $25$, $x$, and $y^4$. We can cancel out these common factors:<br /><br />$\frac{25xy^7}{25xy^4} = \frac{1 \cdot x \cdot y^7}{1 \cdot x \cdot y^4}$<br /><br />Step 2: Simplify the remaining expression<br />After canceling out the common factors, we are left with:<br /><br />$\frac{1 \cdot x \cdot y^7}{1 \cdot x \cdot y^4} = \frac{y^7}{y^4}$<br /><br />To simplify this further, we can use the rule of exponents that states $\frac{a^m}{a^n} = a^{m-n}$:<br /><br />$\frac{y^7}{y^4} = y^{7-4} = y^3$<br /><br />Therefore, the simplified expression is $y^3$.
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