Q. Simplify. Express your answer using positive exponents.5n⋅n5n7
Write Expression & Identify Like Terms: Write down the given expression and identify like terms.The given expression is 5n×n5n7. We can see that there are like terms in the numerator and the denominator that can be simplified.
Simplify by Canceling Common Factors: Simplify the expression by canceling out common factors. The 5 in the numerator and the 5 in the denominator can be canceled out because they are common factors. Also, we can simplify the powers of n by subtracting the exponents in the denominator from the exponent in the numerator. 5n⋅n5n7=n⋅nn7
Apply Quotient Rule for Exponents: Apply the quotient rule for exponents. The quotient rule states that when dividing like bases, you subtract the exponents. In this case, we have n7 divided by n2 (since n×n=n2). n2n7=n7−2=n5
Write Final Simplified Expression: Write the final simplified expression.After canceling out the common factors and applying the quotient rule for exponents, we are left with:n5
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