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Simplify. Express your answer using positive exponents. \newline7v7v5⋅v\frac{7v}{7v^5 \cdot v}

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Multiply and divide powers: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents. \newline7v7v5⋅v\frac{7v}{7v^5 \cdot v}
  1. Identify Common Base: Write down the given expression and identify the common base for the exponents.\newlineThe given expression is 7v7v5⋅v\frac{7v}{7v^5 \cdot v}. We can see that 'vv' is the common base for the exponents.
  2. Simplify Denominator: Simplify the denominator by multiplying the terms with the same base.\newlineWe have 7v5×v7v^5 \times v in the denominator. When we multiply powers with the same base, we add the exponents.\newline7v5×v=7v5+1=7v67v^5 \times v = 7v^{5+1} = 7v^6
  3. Rewrite Expression: Rewrite the expression with the simplified denominator.\newlineNow the expression is 7v7v6\frac{7v}{7v^6}.
  4. Apply Quotient Rule: Apply the quotient rule for exponents to simplify the expression.\newlineThe quotient rule states that am/an=a(m−n)a^m / a^n = a^{(m-n)} when a≠0a \neq 0.\newlineUsing the quotient rule, we get:\newline7v/7v6=7/7×v(1−6)=1×v−5=v−57v / 7v^6 = 7/7 \times v^{(1-6)} = 1 \times v^{-5} = v^{-5}
  5. Express Answer: Express the answer using positive exponents.\newlineSince we want the answer with positive exponents, we rewrite v−5v^{-5} as 1v5\frac{1}{v^5}.

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