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Popular >

simplify (y^x*y^{-x})^4

Solution

simplify

(y^{x} \cdot y^{- x})^{4}

Solution

1

Solution steps

(y^{x} y^{- x})^{4}

Apply exponent rule:

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

(y^{x} y^{- x})^{4} = (y^{x})^{4} (y^{- x})^{4}

= (y^{x})^{4} (y^{- x})^{4}

Apply exponent rule:

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

assuming

a \geq 0

(y^{x})^{4} = y^{x \cdot 4}

= y^{x \cdot 4} (y^{- x})^{4}

Simplify

(y^{- x})^{4} : \frac{1}{y ^{x \cdot 4}}

= y^{x \cdot 4} \frac{1}{y ^{x \cdot 4}}

y^{x \cdot 4} \frac{1}{y ^{x \cdot 4}} = 1

= 1

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Frequently Asked Questions (FAQ)

What is (y^x*y^{-x})^4 ?
The solution to (y^x*y^{-x})^4 is 1