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Simplify. Express your answer using positive exponents. \newline10t6(10t9)(t)\frac{10t^6}{(10t^9)(t)}

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Multiply and divide powers: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents. \newline10t6(10t9)(t)\frac{10t^6}{(10t^9)(t)}
  1. Combine and simplify terms: Combine the terms in the denominator and simplify the expression. \newline10t610t9⋅t\frac{10t^6}{10t^9 \cdot t} \newline= 10t610t9+1\frac{10t^6}{10t^{9+1}} \newline= 10t610t10\frac{10t^6}{10t^{10}}
  2. Apply quotient rule for exponents: Simplify the fraction by canceling out common terms and applying the quotient rule for exponents.\newline=1010×t6t10= \frac{10}{10} \times \frac{t^6}{t^{10}}\newline=1×t6−10= 1 \times t^{6-10}\newline=t−4= t^{-4}
  3. Convert negative exponent: Convert the negative exponent to a positive exponent by rewriting t−4t^{-4}. \newline= 1t4\frac{1}{t^4}

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