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Mandarinka [93]
3 years ago
11

Which expressions are equivalent to this exponential expression

Mathematics
1 answer:
wariber [46]3 years ago
3 0

Answer:

\dfrac{5^4\times 5^{-2}}{5^3}=\dfrac{1}{5}

A is correct.

Step-by-step explanation:

Given: \dfrac{5^4\times 5^{-2}}{5^3}

We are given a exponential expression and to simplify it.

Exponent Law:

  • Product Rule: a^m\times a^n=a^{m+n}
  • Quotient Rule: a^m\div a^n=a^{m-n}
  • Negative Exponent:  a^{-m}=\dfrac{1}{a^m}

\Rightarrow \dfrac{5^4\times 5^{-2}}{5^3}

Using Quotient rule

\Rightarrow 5^{4-3}\times 5^{-2}

\Rightarrow 5^{1}\times 5^{-2}

Using Product Rule

\Rightarrow 5^{1-2}

\Rightarrow 5^{-1}

Using Negative exponent law

\Rightarrow \dfrac{1}{5}

Therefore,  \dfrac{5^4\times 5^{-2}}{5^3}=\dfrac{1}{5}

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