QuestionEXERCISE
1. UME 2906 Que 25 simplify (25) $\frac{1}{x} \times(27)^{\prime}+(121)^{-\frac{1}{2}} \times(625)^{-\frac{1}{4}}$

Studdy Solution

STEP 1

1. We are asked to simplify the given expression.
2. The expression involves exponents and roots that can be simplified using exponent rules.
3. The notation $(27)^{\prime}$ is assumed to mean the derivative of a constant, which is zero.

STEP 2

1. Simplify each term in the expression separately.
2. Combine the simplified terms to achieve the final simplified expression.

STEP 3

Simplify the first term $\frac{1}{x} \times (27)^{\prime}$ .
Since $(27)^{\prime}$ is the derivative of a constant, it equals zero:
$\frac{1}{x} \times 0 = 0$

STEP 4

Simplify the second term $(121)^{-\frac{1}{2}} \times (625)^{-\frac{1}{4}}$ .
First, simplify $(121)^{-\frac{1}{2}}$ :
$(121)^{-\frac{1}{2}} = \frac{1}{\sqrt{121}} = \frac{1}{11}$
Next, simplify $(625)^{-\frac{1}{4}}$ :
$(625)^{-\frac{1}{4}} = \frac{1}{\sqrt[4]{625}} = \frac{1}{5}$
Now, multiply the simplified terms:
$\frac{1}{11} \times \frac{1}{5} = \frac{1}{55}$

STEP 5

Combine the simplified terms from STEP_1 and STEP_2:
$0 + \frac{1}{55} = \frac{1}{55}$
The simplified expression is:
$\boxed{\frac{1}{55}}$

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