Question

Need help answering this one

Answer 1

Option A:

The value $\frac{ 64}{49} }$ is equivalent to the given expression.

Solution:

To find which value is equivalent  to the given expression:

Let us first simplify the given expression.

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

Cancel the common factors.

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

Using exponent rule: $a^0=1$

$\left(\frac{ 8}{ 7}\right)^{2} \times\left(\frac{1}{7^{-3}}\right)^{3} \times 7^{-9}$

$\frac{ 8^{2} }{ 7^{2} }\times\frac{1^{3} }{(7^{-3})^{3} }\times 7^{-9}$

Using exponent rule: $(a^m)^n=a^{mn}$ in the denominator

$\frac{ 8^{2} }{ 7^{2} }\times\frac{1^{3} }{7^{-9} }\times 7^{-9}$

$\frac{ 64}{49} }\times\frac{1 }{7^{-9} }\times 7^{-9}$

Using exponent rule: $\frac{1}{a^m} =a^{-m}$

$\frac{ 64}{49} }\times7^9\times 7^{-9}$

Using exponent rule: $a^m\times a^{-m} =1$

$\frac{ 64}{49} }\times1$

$\Rightarrow\frac{ 64}{49} }$

Option A is the correct answer.

Hence $\frac{ 64}{49} }$ is equivalent to the given expression.