Question

I dont understand how do this question.


There is a picture.​

Answer 1

9514 1404 393

Answer:

b⁶

Explanation:

The question tells you how to work it: use the relations you studied.

Here, you have the power of an expression with an exponent. The exponents multiply.

`\text{Rule: }(a^b)^c=a^(bc)\\\\\text{Appication: }(b^3)^2=b^(3\cdot2)=\boxed{b^6}`

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Additional comment

A coefficient is used to indicate repeated addition: 3x = x + x + x.

An exponent is used to indicate repeated multiplication: x³ = x·x·x.

This is still true when the exponent is applied to an expression with an exponent:

(b³)² = (b³)(b³) . . . . the factor b³ is repeated 2 times as indicated by the exponent 2

Of course, each of these indicates repeated multiplication, so we really have ...

(b³)(b³) = (b·b·b)·(b·b·b) = b·b·b·b·b·b

And this can be simplified using an exponent to show the repeated multiplication:

= b⁶

Then, by going the long way around, we arrive at ...

(b³)² = b⁶