Use the exponent rule to simplify the expression. Assume the variable represents nonzero real numbers.
(m^5m)^-7/(m^-32n^8)
(m^5)*m = m^5*m^1 = m^(5+1) = m^6
(m^6)^-7 = m^(6*-7)=m^(-42)
m^(-42)/(m^(-32)*n^8) =
m^(-42-(-32))*n^(-8) =
m^(-10)*n^(-8) (=ANSWER)
To simplify the expression (m^5m)^-7 / (m^-32n^8), we can use the exponent rule that states (a^m)^n = a^(m*n) for any nonzero real number a.
First, let's simplify the numerator (m^5m)^-7:
(m^5m)^-7 can be written as m^(5*-7)m^(-1*-7) since (a^m)^n = a^(m*n).
Simplifying further, we have m^(-35)m^7.
Next, let's simplify the denominator m^-32n^8:
We can rewrite the denominator as m^-32 * n^8.
Now, when dividing two variables with the same base but different exponents, we subtract the exponents. So, we have m^(-35 + 32) * n^8.
Simplifying further, we get m^(-3) * n^8.
Putting it all together, the simplified expression is:
(m^(-35) * m^7) / (m^(-3) * n^8)
Using the rule a^m / a^n = a^(m-n), we can simplify this expression even further:
m^(-35-7) / (m^-3 * n^8)
Simplifying the exponents, we have:
m^(-42) / (m^-3 * n^8)
Now, using the rule a^m * a^n = a^(m+n), we can rewrite the denominator:
m^(-42) / m^(-3+8) * n^8
Simplifying the exponents, we have:
m^(-42) / m^5 * n^8
Finally, using the rule a^m / a^n = a^(m-n), we can simplify the expression further:
m^(-42-5) * n^8
Simplifying the exponents, we get:
m^(-47) * n^8
Therefore, the simplified expression is m^(-47) * n^8.