Simplify the following exponential expression: \(\left(m^{0}\right)\left(m^{3 / 2}\right)^{5} /\left(m^{8}\right) /\left(m^{1 / 2}\right)\)
Explanation
Simplify the numerator first.
Take note that a number raised to the power of 0 is equal to 1.
So \(m^{0}=1\).
To raise a number with an exponent to another power, simply copy the number and multiply the exponents.
Thus, \(\left(m^{3 / 2}\right)^{5}=m^{15 / 2}\).
Simplify the denominator next.
To divide similar variables with different exponents, simply copy the variable and subtract the exponents:
\(m^{8} /\left(m^{1 / 2}\right)=m^{7.5}\) .
Going back to the original expression and plugging the simplified numerator and denominator, we have:
\(m^{15 / 2} / m^{7.5}=m^{7.5} / m^{7.5}=1\)
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