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Simplify. \newlineExpress your answer using positive exponents.\newline r5⋅r8r^5 \cdot r^8

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Full solution

Q. Simplify. \newlineExpress your answer using positive exponents.\newline r5⋅r8r^5 \cdot r^8
  1. Identify operation: Identify the operation to perform with the exponents.\newlineWhen multiplying two powers that have the same base, we add the exponents according to the exponent rule am×an=a(m+n)a^m \times a^n = a^{(m + n)}.
  2. Apply exponent rule: Apply the exponent rule to r5⋅r8r^5 \cdot r^8.\newlineAdd the exponents 55 and 88 together to get a new exponent for rr.\newliner5⋅r8=r(5+8)r^5 \cdot r^8 = r^{(5 + 8)}
  3. Perform addition of exponents: Perform the addition of the exponents.\newlineCalculate 5+85 + 8 to get 1313.\newliner(5+8)=r13r^{(5 + 8)} = r^{13}

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