Question

what is the value of (-3/7) whole power -4?​

Answer 1

Answer:

(-3/7)^-4

={7/-3)4

=2401/81

Answer 2

Given:

Expression $(-\frac{3}{7}) ^{-4}$

To  FInd:

Value of the expression using properties of exponents.

Solution:

For solving this expression we are going to use the following properties of exponents

1. Negative exponent on a number is reciprocal of the base raised to the same exponent with a positive sign.                                                      $a^{-n}=\frac{1}{a^n}$  
2. Raising a rational number to a power $n$ is the same as the numerator raised to $n$ divided by the denominator raised to $n$.

        $(\frac{a}{b})^n=\frac{(a)^n}{(b)^n}$

Now, starting with the problem,

    $(-\frac{3}{4} )^{-4}$ $=(-\frac{4}{3} )^{4}$          ...(Using property 1)

                $=\frac{(-4)^4}{(3)^4}$            ...(Using property 2)

                $=\frac{(-4)*(-4)*(-4)*(-4)}{(3)*(3)*(3)*(3)}$

                $=\frac{256}{81}$.

Hence, the value of the expression $=\frac{256}{81}$.