Which value is equivalent to 8 multiplied by 4 multiplied by 2 whole over 8 multiplied by 7, the whole raised to the power of 2 multiplied by 8 to the power of 0 over 7 to the power of negative 3, whole to the power of 3 multiplied by 7 to the power of negative 9?

64 over 49

8 over 49

16 over 7

512 over 7

First Option is correct.

Step-by-step explanation:

Since we have given that

8 multiplied by 4 multiplied by 2 whole over 8 multiplied by 7, the whole raised to the power of 2 multiplied by 8 to the power of 0 over 7 to the power of negative 3, whole to the power of 3 multiplied by 7 to the power of negative 9.

It means

So, when we cancel out 8 from numerator and denominator form the first expression, we get

As we know that the exponential rule :

and

And

By applying such rule, we get,

Hence, First Option is correct.

The value is equivalent to 64 over 49

Let's recall following formula about Exponents and Surds:

Let us tackle the problem.

First, we will change this "word problem" into mathematical equation.

8 multiplied by 4 multiplied by 2 ↓

The whole over 8 multiplied by 7 ↓

The whole raised to the power of 2 ↓

The whole multiplied by 8 to the power of 0 over 7 to the power of negative 3, whole to the power of 3 ↓

The whole multiplied by 7 to the power of negative 9 ↓

Grade: High School

Subject: Mathematics

Chapter: Exponents and Surds

Keywords: Power , Multiplication , Division , Exponent , Surd , Negative , Postive , Value , Equivalent