Simplify the expression: (15x⁵y⁶z) / (5x⁻³y⁴z)
Understand the Problem
The question asks to simplify the expression: (15x⁵y⁶z) / (5x⁻³y⁴z). This involves dividing the coefficients and using the rules of exponents to simplify the variables.
Answer
$3x^8y^2$
Answer for screen readers
$3x^8y^2$
Steps to Solve
- Divide the coefficients
Divide the numerical coefficients: $15 / 5 = 3$.
- Simplify the x terms
Use the rule $x^a / x^b = x^{a-b}$ to simplify the $x$ terms: $x^5 / x^{-3} = x^{5 - (-3)} = x^{5+3} = x^8$.
- Simplify the y terms
Use the rule $y^a / y^b = y^{a-b}$ to simplify the $y$ terms: $y^6 / y^4 = y^{6-4} = y^2$.
- Simplify the z terms
Use the rule $z^a / z^b = z^{a-b}$ to simplify the $z$ terms: $z / z = z^{1-1} = z^0 = 1$.
- Combine the simplified terms
Multiply the simplified terms together: $3 \cdot x^8 \cdot y^2 \cdot 1 = 3x^8y^2$.
$3x^8y^2$
More Information
The simplified expression is $3x^8y^2$. Note that any variable to the power of 0 equals 1.
Tips
A common mistake is forgetting the rules of exponents, especially when dealing with negative exponents. For example, when dividing terms with the same base, you subtract the exponents. Also, people may forget that a variable divided by itself simplifies to 1.
AI-generated content may contain errors. Please verify critical information
