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Popular >

simplify sqrt((cos^2(x))^3)

Solution

simplify

(cos^{2} (x))^{3}

Solution

cos^{3} (x)

Solution steps

(cos^{2} (x))^{3}

Apply radical rule:

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

= ((cos^{2} (x))^{3})^{\frac{1}{2}}

Apply exponent rule:

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

assuming

a \geq 0

= (cos^{2} (x))^{3 \cdot \frac{1}{2}}

3 \cdot \frac{1}{2} = \frac{3}{2}

= (cos^{2} (x))^{\frac{3}{2}}

Apply exponent rule:

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

assuming

a \geq 0

= cos^{2 \cdot \frac{3}{2}} (x)

2 \cdot \frac{3}{2} = 3

= cos^{3} (x)

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Frequently Asked Questions (FAQ)

What is sqrt((cos^2(x))^3) ?
The solution to sqrt((cos^2(x))^3) is cos^3(x)