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When multiplying exponents with same base we can add the exponents
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$\sec\left(x\right)^{4}$
Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression sec(x)^2sec(x)^2. When multiplying exponents with same base we can add the exponents. Apply the trigonometric identity: \sec\left(\theta \right)=\sqrt{1+\tan\left(\theta \right)^2}. Simplify \left(\sqrt{1+\tan\left(x\right)^2}\right)^{4} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{2} and n equals 4. Multiply \frac{1}{2} times 4.