To simplify the expression [tex]\( 3x^5 y^4 \div x^2 y \)[/tex], follow these steps:
1. Rewrite the division in fractional form:
[tex]\[
3x^5 y^4 \div x^2 y = \frac{3x^5 y^4}{x^2 y}
\][/tex]
2. Simplify the exponents of [tex]\( x \)[/tex]:
- Apply the properties of exponents: [tex]\(\frac{x^a}{x^b} = x^{a-b}\)[/tex].
- For the [tex]\( x \)[/tex] terms, this becomes:
[tex]\[
\frac{x^5}{x^2} = x^{5-2} = x^3
\][/tex]
3. Simplify the exponents of [tex]\( y \)[/tex]:
- Similarly, apply the properties of exponents to the [tex]\( y \)[/tex] terms:
[tex]\[
\frac{y^4}{y} = y^{4-1} = y^3
\][/tex]
4. Combine the simplified components:
- Substitute the simplified [tex]\( x \)[/tex] and [tex]\( y \)[/tex] terms back into the expression:
[tex]\[
\frac{3x^5 y^4}{x^2 y} = 3 \cdot x^3 \cdot y^3
\][/tex]
So, the simplified expression is:
[tex]\[
3x^3y^3
\][/tex]
Thus, [tex]\( 3x^5 y^4 \div x^2 y \)[/tex] simplifies to [tex]\( 3x^3 y^3 \)[/tex].
