Simplifying Exponential Expressions

The video tutorial explains how to simplify a complex mathematical expression involving exponents. It begins by introducing the problem and then focuses on simplifying the denominator by reordering and multiplying numbers. The tutorial demonstrates how to combine exponents with the same base by adding them. Finally, it simplifies the expression into scientific notation and verifies the result, ensuring the number is between 1 and 9, multiplied by a power of 10.

What is the initial expression that needs to be simplified?

• 7 times 10 to the fifth over 2 times 10 to the negative 2 times 2.5 times 10 to the ninth

• 5 times 10 to the fourth over 3 times 10 to the negative 3 times 2 times 10 to the eighth

• 6 times 10 to the sixth over 4 times 10 to the negative 1 times 3 times 10 to the seventh

• 8 times 10 to the third over 5 times 10 to the negative 4 times 1.5 times 10 to the tenth

What is the result of multiplying 2 by 2.5 in the denominator?

• 5

• 7

• 6

• 4

How do you simplify 10 to the negative 2 times 10 to the ninth?

• By dividing the exponents to get 10 to the fourth

• By adding the exponents to get 10 to the eleventh

• By subtracting the exponents to get 10 to the seventh

• By multiplying the exponents to get 10 to the eighteenth

What operation is used to combine exponents when multiplying numbers with the same base?

• Multiplication

• Subtraction

• Addition

• Division

What is the purpose of reordering the terms in the denominator?

• To make the expression more complex

• To increase the value of the expression

• To simplify the multiplication process

• To change the base of the exponents

What is the simplified form of 7 divided by 5?

• 1.5

• 1.4

• 1.3

• 1.2

How do you simplify 10 to the fifth divided by 10 to the seventh?

• By adding the exponents to get 10 to the twelfth

• By subtracting the exponents to get 10 to the negative 2

• By multiplying the exponents to get 10 to the thirty-fifth

• By dividing the exponents to get 10 to the second

What is the result of 10 to the 5 minus 7?

• 10 to the 0

• 10 to the negative 1

• 10 to the 1

• 10 to the negative 2

What is the final simplified form of the expression?

• 2.4 times 10 to the negative 3

• 1.4 times 10 to the negative 2

• 3.4 times 10 to the negative 4

• 4.4 times 10 to the negative 5

What is the condition for a number to be in scientific notation?

• The number must be less than 0

• The number must be greater than 10

• The number must be between 0 and 1

• The number must be between 1 and 9