After using the property of power, the expressions as a power of the number a is $(a^3)^{-2} = a^{-6}$ , $(a^{-1}\cdot a^{-2})^{-3} = a^{9}$ and $((a^2)^{-2})^2=a^{-8}$ .

In the given question we have to solve the given expressions as a power of the number a where a≠0.

The first given expression is $(a^3)^{-2}$ .

Using the property of multiplication of power; $(a^m)^n=a^{mn}$ .

Simplifying the expression.

$(a^3)^{-2} = a^{3*(-2)}$

$(a^3)^{-2} = a^{-6}$

The second expression is $(a^{-1}\cdot a^{-2})^{-3}$

Using the property of multiplication of power; $(a^m)^n=a^{mn}$ .

$(a^{-1}\cdot a^{-2})^{-3} = a^{(-1)\times(-3)}\cdot a^{(-2)\times(-3)}$

$(a^{-1}\cdot a^{-2})^{-3} = a^{3}\cdot a^{6}$

Using the property of sum of power $a^m\cdot a^n=a^{m+n}$

$(a^{-1}\cdot a^{-2})^{-3} = a^{(3+6)}$

$(a^{-1}\cdot a^{-2})^{-3} = a^{9}$

The third expression is $((a^2)^{-2})^2$ .

Using the property of multiplication of power; $(a^m)^n=a^{mn}$ .

$((a^2)^{-2})^2=((a^2)^{(-2)\times2})$

$((a^2)^{-2})^2=(a^2)^{-4}$

Again using the property of multiplication of power; $(a^m)^n=a^{mn}$ .

$((a^2)^{-2})^2=a^{2\times(-4)}$

$((a^2)^{-2})^2=a^{-8}$

To learn more about property of power link is here

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7 0

1 year ago

Find the solutions to the equation below. Check all that apply.

lubasha [3.4K]

2x^2 + 9x + 4 = 0

x^2 + 9/2*x + 2 = 0

x = - 9/4 +- √(81/16 - 32/16) = - 9/4 +- 7/4

x1 = - 1/2

x2 = - 4

5 0

4 years ago

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