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Popular >

simplify sqrt((4(cos^2(x)))^3)

Solution

simplify

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

Solution

8 cos^{3} (x)

Solution steps

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

Apply radical rule:

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

= ((4 cos^{2} (x))^{3})^{\frac{1}{2}}

Apply exponent rule:

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

assuming

a \geq 0

= (4 cos^{2} (x))^{3 \cdot \frac{1}{2}}

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

= (4 cos^{2} (x))^{\frac{3}{2}}

Apply exponent rule:

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

= 4^{\frac{3}{2}} (cos^{2} (x))^{\frac{3}{2}}

4^{\frac{3}{2}} = 8

= 8 (cos^{2} (x))^{\frac{3}{2}}

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

= 8 cos^{3} (x)

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Frequently Asked Questions (FAQ)

What is sqrt((4(cos^2(x)))^3) ?
The solution to sqrt((4(cos^2(x)))^3) is 8cos^3(x)