Question

simplify the expression.
\frac{10^{19/4}}{10^{3/4}}

Explanation:

Step1: Use exponent rule for division

When dividing exponents with the same base, we subtract the exponents: \( \frac{a^m}{a^n} = a^{m - n} \). Here, the base is 10, so \( \frac{10^{\frac{19}{4}}}{10^{\frac{3}{4}}} = 10^{\frac{19}{4}-\frac{3}{4}} \)

Step2: Subtract the fractions

Subtract the exponents: \( \frac{19}{4}-\frac{3}{4}=\frac{19 - 3}{4}=\frac{16}{4} = 4 \)

Step3: Simplify the exponent

So \( 10^{\frac{16}{4}}=10^4 \)

Step4: Calculate \( 10^4 \)

\( 10^4 = 10\times10\times10\times10 = 10000 \)

Answer:

10000