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Popular >

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

Solution

simplify

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

Solution

sec^{3} (x)

Solution steps

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

Apply radical rule:

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

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

Apply exponent rule:

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

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

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

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

Apply exponent rule:

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

assuming

a \geq 0

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

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

= sec^{3} (x)

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Frequently Asked Questions (FAQ)

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