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Q.

Which of the following is the answer of $\frac{25 \times t^{- 4}}{5^{- 3} \times 10 \times t^{- 8}}$ ?

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a

\frac{625 \times t^{4}}{2}

b

\frac{635 \times t^{4}}{2}

c

\frac{625 \times t^{4}}{3}

d

\frac{625 \times t^{}}{2}

answer is A.

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Detailed Solution

Concept- We will comprehend how to simplify the powers of the several numbers involved in the problem before presenting the solution in as few words as we can.
In mathematics, there are numerous different kinds of operators. The four most fundamental operators are multiplication, division, addition, and subtraction. These operators allow us to simplify an expression to the smallest degree possible in relation to the respective numbers by performing specific operations.
In fractional form, simplification simply refers to the presentation of the statement using the fewest terms possible that are free of radicals (powers).

\frac{25 \times t^{- 4}}{5^{- 3} \times 10 \times t^{- 8}}

=

\frac{5 \times 5 \times t^{- 4}}{5^{- 3} \times 2 \times 5 \times t^{- 8}}

= \frac{5 \times t^{- 4}}{5^{- 3} \times 2 \times t^{- 8}}

Now, using the power division formula, we attempt to lower each term's powers.

\frac{a^{m}}{a^{n}} = a^{m - n}

=

\frac{5^{1 - (- 3)} \times t^{- 4 - (- 8)}}{2}

=

\frac{5^{1 + 3} \times t^{- 4 - (- 8)}}{2}

=

\frac{5^{4} \times t^{4}}{2}

=

\frac{625 \times t^{4}}{2}

Hence, the correct answer is option 1)

\frac{625 \times t^{4}}{2}

.

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