(d) Simplify $$ \frac{a^{\frac{3}{4}} imes a^{-\frac{1}{2}}}{a^{\frac{1}{4}}} $$.

Question

(d) Simplify $$ \frac{a^{\frac{3}{4}} 	imes a^{-\frac{1}{2}}}{a^{\frac{1}{4}}} $$.

UpStudy AI · Accepted Answer

1. Combine the powers in the numerator using the rule $$ a^m \times a^n = a^{m+n} $$:
   $$
   a^{\frac{3}{4}} \times a^{-\frac{1}{2}} = a^{\frac{3}{4} - \frac{1}{2}}.
   $$

2. Simplify the exponent in the numerator:
   $$
   \frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4}.
   $$
   The expression now becomes:
   $$
   \frac{a^{\frac{1}{4}}}{a^{\frac{1}{4}}}.
   $$

3. Use the quotient rule for exponents $$ \frac{a^m}{a^m} = a^{m-m} = a^0 $$:
   $$
   a^{\frac{1}{4} - \frac{1}{4}} = a^0.
   $$

4. Since $$ a^0 = 1 $$ (provided $$ a \neq 0 $$), the simplified expression is:
   $$
   1.
   $$
The simplified expression is $$ 1 $$.

(d) Simplify .

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