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Popular >

simplify sqrt((-rΔqΔ)^r)

Solution

simplify

(- r Δ q Δ)^{r}

Solution

i^{r} Δ^{r} (r q)^{\frac{r}{2}}

Solution steps

(- r Δ q Δ)^{r}

Apply radical rule:

a = a^{\frac{1}{2}}

= ((- r Δ q Δ)^{r})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

= (- r Δ q Δ)^{r \frac{1}{2}}

Simplify

r \frac{1}{2} : \frac{r}{2}

= (- r Δ q Δ)^{\frac{r}{2}}

Simplify

- r Δ q Δ : - Δ^{2} r q

= (- Δ^{2} r q)^{\frac{r}{2}}

Apply exponent rule:

(- a)^{\frac{m}{n}} = (- 1)^{\frac{m}{n}} (a)^{\frac{m}{n}}

(- r q Δ^{2})^{\frac{r}{2}} = (- 1)^{\frac{r}{2}} (r q Δ^{2})^{\frac{r}{2}}

= (- 1)^{\frac{r}{2}} (Δ^{2} r q)^{\frac{r}{2}}

(- 1)^{\frac{r}{2}} = i^{r}

= i^{r} (r q Δ^{2})^{\frac{r}{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(Δ^{2} r q)^{\frac{r}{2}} = (Δ^{2})^{\frac{r}{2}} (r q)^{\frac{r}{2}}

= i^{r} (Δ^{2})^{\frac{r}{2}} (r q)^{\frac{r}{2}}

(Δ^{2})^{\frac{r}{2}} : Δ^{r}

= i^{r} Δ^{r} (r q)^{\frac{r}{2}}

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Frequently Asked Questions (FAQ)

What is sqrt((-rΔqΔ)^r) ?
The solution to sqrt((-rΔqΔ)^r) is i^rΔ^r(rq)^{r/2}