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beks73 [17]
1 year ago
9

PLEASE HELP ASAP!! Represent the following expressions as a power of the number a where a≠0.

Mathematics
1 answer:
Step2247 [10]1 year ago
7 0

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

brainly.com/question/28747844

#SPJ1

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