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

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

\((\frac{8\times 4\times 2}{8\times 7})^{2} \times (\frac{8^0}{7^{-3}})^3 \times 7^{-9}\)

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

\((\frac{ 4\times 2}{7})^{2} \times (\frac{8^0}{7^{-3}})^3 \times 7^{-9}\)

\(=\frac{8^2}{7^2}\times \frac{8^0}{7^{-3}}\times 7^{-9}\)

As we know that the exponential rule :

\((\frac{a}{b})^m=\frac{a^m}{b^m}\)

and

\((a^m)^n=a^{mn}\)

And

\(a^0=1\)

By applying such rule, we get,

\(\frac{8^2}{7^2}\times \frac{8^0}{7^{-3}}\times 7^{-9}\\\\=\frac{64}{49}\times \frac{1}{7^{-9}}\times 7^{-9}\\\\=\frac{64}{49}\times \frac{7^{-9}}{7^{-9}}\\\\=\frac{64}{49}\)

Hence, First Option is correct.

johanrusli johanrusli · Answer 2 · 2019-07-25T03:43:01-04:00

The value is equivalent to 64 over 49

Further explanation

Let's recall following formula about Exponents and Surds:

\(\boxed { \sqrt { x } = x ^ { \frac{1}{2} } }\)

\(\boxed { (a ^ b) ^ c = a ^ { b . c } }\)

\(\boxed {a ^ b \div a ^ c = a ^ { b - c } }\)

\(\boxed {\log a + \log b = \log (a \times b) }\)

\(\boxed {\log a - \log b = \log (a \div b) }\)

Let us tackle the problem.

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

8 multiplied by 4 multiplied by 2 ↓

\(8 \times 4 \times 2 = 64\)

The whole over 8 multiplied by 7 ↓

\(64 \div (8 \times 7) = 64 \div 56 = 8 \div 7\)

The whole raised to the power of 2 ↓

\(( 8 \div 7 )^2\)

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

\((\frac{8}{7})^2 \times (\frac{8^0}{7^{-3}})^3\)

\((\frac{8}{7})^2 \times (\frac{1}{7^{-9}})\)

\((\frac{8^2}{7^2}) \times (\frac{1}{7^{-9}})\)

\(\frac{8^2}{7^{-7}}\)

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

\(\frac{8^2}{7^{-7}} \times 7^{-9}\)

\(\frac{8^2}{7^2}\)

\(\large {\boxed {\frac{64}{49} } }\)

Learn more

Coefficient of A Square Root : https://brainly.com/question/11337634
The Order of Operations : https://brainly.com/question/10821615
Write 100,000 Using Exponents : https://brainly.com/question/2032116

Answer details

Grade: High School

Subject: Mathematics

Chapter: Exponents and Surds

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