To find the exponent in an equivalent form to the expression \( 1^1 \times 1^3 \), we start by simplifying the expression:
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Recall that any non-zero number raised to a power is equal to itself. Thus, we have: \[ 1^1 = 1 \] and \[ 1^3 = 1. \]
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Now, multiply these two results: \[ 1^1 \times 1^3 = 1 \times 1 = 1. \]
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Since the product is \( 1 \), we can express this in an equivalent form using exponents: \[ 1 = 1^x \] for any exponent \( x \).
In conclusion, since \( 1 \) raised to any power is still \( 1 \), there is no specific exponent that uniquely represents the equivalent form except that it can be expressed as \( 1^x \) for any \( x \). Thus, we can say that the exponent is any real number (commonly denoted as \( x \)).
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