Simplify. Express your answer using proper exponents. 7a^5b^3c / 7ab^4c^8
Understand the Problem
The question is asking to simplify the expression which involves dividing two algebraic terms and expressing the result using proper exponents. This involves applying the laws of exponents to the expression provided.
Answer
$$ \frac{a^4}{bc^7} $$
Answer for screen readers
$$ \frac{a^4}{bc^7} $$
Steps to Solve
- Simplify the coefficients
Divide the coefficients (numbers) separately: $$ \frac{7}{7} = 1 $$
- Simplify the variable (a)
Subtract the exponent of (a) in the denominator from the exponent in the numerator: $$ a^{5-1} = a^4 $$
- Simplify the variable (b)
Subtract the exponent of (b) in the denominator from the exponent in the numerator: $$ b^{3-4} = b^{-1} $$
- Simplify the variable (c)
Subtract the exponent of (c) in the denominator from the exponent in the numerator: $$ c^{1-8} = c^{-7} $$
- Combine the simplified terms
Combine all the simplified terms together into one expression: $$ 1 \times a^4 \times b^{-1} \times c^{-7} = a^4 \frac{1}{b} \frac{1}{c^7} = \frac{a^4}{bc^7} $$
$$ \frac{a^4}{bc^7} $$
More Information
The result represents the simplified form of the given expression, showing the relationship between the variables and their exponents clearly. When a variable's exponent is negative, it indicates that variable should be moved to the denominator.
Tips
- Forgetting to subtract exponents correctly can lead to incorrect simplification.
- Neglecting to express terms with negative exponents properly in the final answer.
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