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Im cant figure out how to do this one ((-3)^2)^-3

User Mrek
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1 Answer

2 votes

Answer:


(1)/(729)

Explanation:


\left(\frac{}{}(-3)^2\frac{}{}\right)^(-3)

First, we should evaluate inside the large parentheses:


(-3)^2 = (-3)\cdot (-3) = 9

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,


4^3 = 4 \, \cdot\, 4\, \cdot \,4

↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where
(-3)^2 was originally:


(9)^(-3)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,


3^(-2) = (1)/(3^2) = (1)/(3\cdot 3) = (1)/(9)

Finally, we can apply this principle to the
9^(-3):


9^(-3) = (1)/(9^3) = \boxed{(1)/(729)}

User Vikbert
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