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If p = (x^(a+ b))/(x^b), what is the val...

If `p = (x^(a+ b))/(x^b)`, what is the value of positive integer p?
(1) `x = 5`
(2) `a = 0`

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The correct Answer is:
To solve for \( p \) given the equation \( p = \frac{x^{a+b}}{x^b} \), we can simplify the expression step by step using the values provided. ### Step 1: Substitute the values of \( x \) and \( a \) Given: - \( x = 5 \) - \( a = 0 \) We can substitute these values into the equation: \[ p = \frac{5^{0+b}}{5^b} \] ### Step 2: Simplify the exponent Since \( a = 0 \), we can rewrite \( 0 + b \) as just \( b \): \[ p = \frac{5^b}{5^b} \] ### Step 3: Apply the property of exponents Using the property of exponents that states \( \frac{x^m}{x^n} = x^{m-n} \), we can simplify further: \[ p = 5^{b-b} \] ### Step 4: Simplify the exponent Since \( b - b = 0 \): \[ p = 5^0 \] ### Step 5: Calculate the value of \( 5^0 \) Any non-zero number raised to the power of 0 is 1: \[ p = 1 \] ### Final Answer Thus, the value of the positive integer \( p \) is: \[ \boxed{1} \]
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