simplify 24m^6 / (6m^15) * 5m^7
give your answer in positive exponential form
To simplify 24m^6 / (6m^15) * 5m^7, we can simplify each part individually and then multiply the resulting terms.
First, let's simplify the numerator and denominator separately:
Numerator: 24m^6
Denominator: 6m^15
To simplify the numerator, we don't have any like terms to combine, so it remains as 24m^6.
To simplify the denominator, we can divide 6 by 6 to get 1, and subtract exponents to simplify the m terms:
m^15 / m^6 = m^(15 - 6) = m^9
So, the simplified form of 24m^6 / (6m^15) is (24m^6) / (6m^15) = 4m^(-9).
Now, let's multiply this simplified fraction by 5m^7:
4m^(-9) * 5m^7 = (4 * 5) * (m^(-9) * m^7) = 20 * m^(-9 + 7) = 20 * m^(-2)
Finally, we can write the answer in positive exponential form by moving the negative exponent from the numerator to the denominator:
20 * m^(-2) = 20 * 1/m^2 = 20/m^2.
Therefore, the simplified expression in positive exponential form is 20/m^2.