Question
Simplify the following expression
(14a^4b^6c^-10)/(8a^-2b^3c^-5)
(14a^4b^6c^-10)/(8a^-2b^3c^-5)
Answers
Answer
Simplify the following expression
(14a^4b^6c^-10)/(8a^-2b^3c^-5)
(14a^4b^6c^-10)/(8a^-2b^3c^-5)
Answered by
GPT 3.5
To simplify this expression, we will use the following rules of exponents:
1) When dividing two exponents with the same base, we subtract the exponents.
2) When raising a power to another power, we multiply the exponents.
Using these rules, we can simplify the expression as follows:
(14a^4b^6c^-10)/(8a^-2b^3c^-5)
= (14/8) * (a^4/a^-2) * (b^6/b^3) * (c^-10/c^-5)
= (7/4) * a^(4 - (-2)) * b^(6 - 3) * c^(-10 - (-5))
= (7/4) * a^6 * b^3 * c^-5
Therefore, the simplified expression is (7/4) * a^6 * b^3 * c^-5.
1) When dividing two exponents with the same base, we subtract the exponents.
2) When raising a power to another power, we multiply the exponents.
Using these rules, we can simplify the expression as follows:
(14a^4b^6c^-10)/(8a^-2b^3c^-5)
= (14/8) * (a^4/a^-2) * (b^6/b^3) * (c^-10/c^-5)
= (7/4) * a^(4 - (-2)) * b^(6 - 3) * c^(-10 - (-5))
= (7/4) * a^6 * b^3 * c^-5
Therefore, the simplified expression is (7/4) * a^6 * b^3 * c^-5.
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