Question

How do you simplify (a3b2)2

Answer 1

9514 1404 393

Answer:

a⁶b⁴

Explanation:

The relevant rules of exponents are ...

(ab)^c = (a^c)(b^c)

(a^b)^c = a^(bc)

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These let us simplify the expression as follows:

`(a^3b^2)^2=(a^3)^2(b^2)^2=a^(3\cdot2)b^(2\cdot2)=\boxed{a^6b^4}`

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Additional comment

It might be helpful to remember that an exponent signifies repeated multiplication.

a·a·a = a³ . . . . . . 'a' is a factor 3 times, so the exponent is 3.

Similarly, ...

(a³)² = (a³)·(a³) = (a·a·a)·(a·a·a) = a⁶

Answer 2

a^6b^4

Explanation:

(a³b²)²

a^6b^4