Convert the expression (p/q)^2/5 to its radical form.

1 answer:

6 0

$\left(\dfrac{p}{q}\right)^\frac{2}{5}=\sqrt[5]{\left(\dfrac{p}{q}\right)^2}=\sqrt[5]{\dfrac{p^2}{q^2}}\\\\Used:\\\\a^\frac{m}{n}=\sqrt[n]{a^m}$

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Find the quotient of (11 ^ 18)/(11 ^ 3)

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Answer:

The first choice, $11^{15}$ .

Step-by-step explanation:

The numerator, $11^{18}$ , is equivalent to eighteen " $11$ " multiplied together:

$11^{18} = \underbrace{11 \times 11 \times 11 \times 11 \times \cdots \times 11 \times 11}_{\text{$18$ in total}}$ .

On the other hand, the denominator, $11^{3}$ , is equivalent to three " $11$ " multiplied with one another:

$11^{3} = 11 \times 11 \times 11$ .

Dividing $11^{18}$ by $11^{3}$ would eliminate three " $11$ " from the numerator:

$\begin{aligned}& \frac{11^{18}}{11^{3}} \\ =\; & \frac{(11 \times 11 \times 11) \times \overbrace{11 \times \cdots \times 11}^{\text{$(18 - 3)$ in total}}}{(11 \times 11 \times 11)} \\ =\; & \overbrace{11 \times \cdots \times 11}^{\text{$15$ in total}} \\ =\; & 11^{15}\end{aligned}$ .