Question

By what should (-4/7)^2 be multiplied to get (49/16)^-2​

Answer 1

The number to be multiplied is $\frac{343}{64}$.

Step-by-step explanation:

Let the number to be multiplied be x.

The expression is:

$(-\frac{4}{7})^{2}\times x=(\frac{49}{16})^{-2}$

Compute the value of x as follows:

$(-\frac{4}{7})^{2}\times x=(\frac{49}{16})^{-2}$

$(-\frac{4}{7})^{2}\times x=((\frac{7}{4}))^{2})^{-2}$

$(\frac{4}{7})^{2}\times x=(\frac{7}{4})$

$x=\frac{7}{4}\times (\frac{7}{4})^{2}$

$x=(\frac{7}{4})^{3}$

$x=\frac{343}{64}$

Thus, the number to be multiplied is $\frac{343}{64}$.

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