Question

(laws of exponents with integer exponents mc) what is the value of the quantity negative one fourth cubed all raised to the power of negative 3? −1 1 −262,144 262,144

Answer 1

The value of the given quantity ((-1/4)^3)^-3 by laws of exponent is -262144.

According to the guven question.

We have a quantity $((\frac{-1}{4}) ^{3}) ^{-3}$.

Since, we have to find the value of above quatity by using laws of exponents.

From the laws of exponents we know that

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

and $x^{-1} = \frac{1}{x}$

Therefore, the value of the given quantity is given by

$((\frac{-1}{4}) ^{3}) ^{-3}$

$= (\frac{-1}{4}) ^{3\times -3}$

= $(\frac{-1}{4}) ^{-9}$

= $\frac{1}{(\frac{-1}{4} )^{9} } }$

= (-4)^9

= -262144

Hence, the value of the given quantity ((-1/4)^3)^-3 by laws of exponent is -262144.

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