Simplify the expression. y 27 y 9 \frac{y^{27}}{y^9}

this problem, we want to simplify the expression y to the twenty seventh power divided by y to the ninth power. In order to do this, we're going to use our quotient rule for exponents. So first, we want to check, do these have the same base value? Yes, they both have a base value of y. So that means we can apply our quotient rule by subtracting the exponents. So we can rewrite this as y to the twenty seven minuteus ninth power, which simplifies to y to the eighteenth power. And this is our expression now in its simplest form.

6. Exponents and Polynomials

The Quotient Rule

Beginning Algebra

6. Exponents and Polynomials

The Quotient Rule

Struggling with Beginning Algebra?

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Multiple Choice

Simplify the expression.
$\frac{y^{27}}{y^{9}}$

$y^3$

$y^{18}$

$\frac{1}{y^{18}}$

$\frac{1}{y^3}$

Verified step by step guidance

Understand the Quotient Rule for Exponents, which states that when you divide two expressions with the same base, you subtract the exponents: $a^{m} \div a^{n} = a^{m-n}$.

Identify the base and the exponents in the given problem. Make sure both terms have the same base to apply the Quotient Rule.

Rewrite the division of the exponential expressions as a single expression with the same base and subtract the exponent in the denominator from the exponent in the numerator.

Simplify the expression by performing the subtraction of the exponents.

If possible, rewrite the result in a simpler form, such as removing any zero exponents or expressing negative exponents as fractions.

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Struggling with Beginning Algebra?

Simplify the expression.y27y9\frac{y^{27}}{y^9}

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Simplify the expression.
$\frac{y^{27}}{y^{9}}$