The value of the expression \((-3)^3 \times (0.3)^{-2} \times 0.01\) lies between which of the following ranges?
-3.5 and -2.5
The expression uses an odd power of a negative number and a negative exponent. An odd power keeps the negative sign, and a negative exponent means the reciprocal: \(a^{-n} = \dfrac{1}{a^n}\).
Step 1 — \((-3)^3 = -27\).
Step 2 — \((0.3)^{-2} = \dfrac{1}{(0.3)^2} = \dfrac{1}{0.09} = \dfrac{100}{9}\).
Step 3 — Multiply: \(-27 \times \dfrac{100}{9} \times \dfrac{1}{100} = -\dfrac{27}{9} = -3\).
The value is \(-3\), which lies between \(-3.5\) and \(-2.5\). It is negative, so the two positive ranges fail, and it is smaller than \(-2.5\), so the range from \(-2.5\) to \(-2.25\) also fails.
-3.5 and -2.5 option is correct.
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