Question Video: Computing Numerical Expressions Using Laws of Exponents | Nagwa Question Video: Computing Numerical Expressions Using Laws of Exponents | Nagwa

# Question Video: Computing Numerical Expressions Using Laws of Exponents Mathematics • Second Year of Preparatory School

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Calculate (10⁵ × 25² × 4)/(20² × 5⁵).

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### Video Transcript

Calculate 10 to the fifth power multiplied by 25 squared multiplied by four divided by 20 squared multiplied by five to the fifth power.

To calculate this expression, we can write the powers in expanded form and then cancel common factors in the numerator and denominator. The first term in the numerator, 10 to the fifth power, can be rewritten as 10 multiplied by 10 multiplied by 10 multiplied by 10 multiplied by 10. 25 squared can be written as 25 multiplied by 25. This means that the entire numerator can be rewritten as shown.

We can do the same with the denominator and rewrite 20 squared and five to the fifth power. Whilst we could cancel at this stage, we can simplify our expression further by writing the numerator and denominator as products of prime factors. We know that 10 is equal to two multiplied by five. 25 can be rewritten as five multiplied by five. We can rewrite four as two multiplied by two. And 20 written as a product of prime factors is two multiplied by two multiplied by five.

We can use the first three of these to rewrite the numerator as shown. And repeating this process with the denominator, we have the following expression. Next, we can cancel common factors. Two multiplied by two multiplied by two multiplied by two can be canceled from the numerator and denominator. We can also cancel seven fives from the numerator and denominator. Our expression therefore simplifies to two multiplied by five multiplied by five multiplied by two multiplied by two all divided by one. This is equal to two cubed multiplied by five squared. And since two cubed is equal to eight and five squared is 25, we have eight multiplied by 25, which is equal to 200. 10 to the fifth power multiplied by 25 squared multiplied by four divided by 20 squared multiplied by five to the fifth power is 200.

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