
Simplify the given expression.
$\dfrac{{25 \times {t^{ - 4}}}}{{{5^{ - 3}} \times 10 \times {t^{ - 4}}}}\left( {t \ne 0} \right)$
Answer
513.6k+ views
Hint – In this question we have to simplify the given equation so look for terms common in both numerator and denominator part, use the basic property of exponential powers like if the base is the same and the number is in multiplication therefore powers get added to get the answer.
Complete step-by-step answer:
Given equation is
$\dfrac{{25 \times {t^{ - 4}}}}{{{5^{ - 3}} \times 10 \times {t^{ - 4}}}}\left( {t \ne 0} \right)$
Now we have to simplify this equation.
First of all cancel out the common terms from numerator and denominator.
So, as we see that $\left( {{t^{ - 4}}} \right)$ is common so cancel out this term we have,
$ \Rightarrow \dfrac{{25 \times {t^{ - 4}}}}{{{5^{ - 3}} \times 10 \times {t^{ - 4}}}} = \dfrac{{25}}{{{5^{ - 3}} \times 10}}$ So, this is the remaining term we have
Now factorize 25 and 10 we have,
$ \Rightarrow \dfrac{{25}}{{{5^{ - 3}} \times 10}} = \dfrac{{5 \times 5}}{{{5^{ - 3}} \times 2 \times 5}}$
So, as we see that 5 is common so cancel out this term we have,
$ \Rightarrow \dfrac{{5 \times 5}}{{{5^{ - 3}} \times 2 \times 5}} = \dfrac{5}{{2 \times {5^{ - 3}}}}$
Now take $\left( {{5^{ - 3}}} \right)$ to numerator we have,
$ \Rightarrow \dfrac{5}{{2 \times {5^{ - 3}}}} = \dfrac{{5 \times {5^3}}}{2}$
Now if the base is the same and the number is in multiplication therefore powers got added.
$ \Rightarrow \dfrac{{5 \times {5^3}}}{2} = \dfrac{{{5^{1 + 3}}}}{2} = \dfrac{{{5^4}}}{2}$
Now as we know ${5^4} = 625$ so, substitute this value in above equation we have,
$ \Rightarrow \dfrac{{25 \times {t^{ - 4}}}}{{{5^{ - 3}} \times 10 \times {t^{ - 4}}}} = \dfrac{{625}}{2} = 312.5$
So, this is the required answer.
Note – Whenever we face such type of problems the key concept is to use basic simplification techniques to get maximum terms canceled, in this problem it’s given that $t \ne 0$, because if we make t zero then this equation will have$\dfrac{0}{0}$, indeterminate form which can’t be solved thus take care of the conditions.
Complete step-by-step answer:
Given equation is
$\dfrac{{25 \times {t^{ - 4}}}}{{{5^{ - 3}} \times 10 \times {t^{ - 4}}}}\left( {t \ne 0} \right)$
Now we have to simplify this equation.
First of all cancel out the common terms from numerator and denominator.
So, as we see that $\left( {{t^{ - 4}}} \right)$ is common so cancel out this term we have,
$ \Rightarrow \dfrac{{25 \times {t^{ - 4}}}}{{{5^{ - 3}} \times 10 \times {t^{ - 4}}}} = \dfrac{{25}}{{{5^{ - 3}} \times 10}}$ So, this is the remaining term we have
Now factorize 25 and 10 we have,
$ \Rightarrow \dfrac{{25}}{{{5^{ - 3}} \times 10}} = \dfrac{{5 \times 5}}{{{5^{ - 3}} \times 2 \times 5}}$
So, as we see that 5 is common so cancel out this term we have,
$ \Rightarrow \dfrac{{5 \times 5}}{{{5^{ - 3}} \times 2 \times 5}} = \dfrac{5}{{2 \times {5^{ - 3}}}}$
Now take $\left( {{5^{ - 3}}} \right)$ to numerator we have,
$ \Rightarrow \dfrac{5}{{2 \times {5^{ - 3}}}} = \dfrac{{5 \times {5^3}}}{2}$
Now if the base is the same and the number is in multiplication therefore powers got added.
$ \Rightarrow \dfrac{{5 \times {5^3}}}{2} = \dfrac{{{5^{1 + 3}}}}{2} = \dfrac{{{5^4}}}{2}$
Now as we know ${5^4} = 625$ so, substitute this value in above equation we have,
$ \Rightarrow \dfrac{{25 \times {t^{ - 4}}}}{{{5^{ - 3}} \times 10 \times {t^{ - 4}}}} = \dfrac{{625}}{2} = 312.5$
So, this is the required answer.
Note – Whenever we face such type of problems the key concept is to use basic simplification techniques to get maximum terms canceled, in this problem it’s given that $t \ne 0$, because if we make t zero then this equation will have$\dfrac{0}{0}$, indeterminate form which can’t be solved thus take care of the conditions.
Recently Updated Pages
Solve the given equation dfrac2xleft 75x right9xleft class 8 maths CBSE

Shaniwarwada Tulsi Baug and Mahatma Phule mandai are class 8 social science CBSE

With additive inverse operations verify that x x f-class-8-maths-CBSE

Fill in the blank with the most appropriate word Does class 8 english CBSE

Solve for x dfrac3x 1 + dfrac1x + 1 dfrac4x where x class 8 maths CBSE

Choose the word that is opposite to the given word class 8 english CBSE

Trending doubts
Write a book review which you have recently read in class 8 english CBSE

When people say No pun intended what does that mea class 8 english CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How many ounces are in 500 mL class 8 maths CBSE

You want to apply for admission into a prestigious class 8 english CBSE

Give a character sketch of Griffin the scientist in class 8 english CBSE
