(4x2)2 (2x3)3 where am I going wrong?

Question

(4x²)² (2x³)³

 

I know the answer should be 128x^13.

here is how I calculated it: 4x⁴ times 2x⁹ equals 8x^13. 

 

Where am I going wrong?

Answer 1

You're on the right track.

First:

(4x²)²

We have 4x² * 4x².the coefficients multiply together to make 16. That leaves us with x² * x². Remember, we add exponents together, and that gives us x⁴.  We're actually doing the same with the coefficient here if you think about it:

4¹ * 4¹ = 4², which is 16.

So right now we have 16x⁴.

 

Next we have 2x³ * 2x³ * 2x³

2 * 2 * 2 = 8, and

x³ * x³ * x³ = x⁹

giving us 8x⁹

 

16 * 8 = 128

x⁴ * x⁹ = x¹³

That leads to the final answer of 128x¹³.

 

Where you tripped up is that you focused the outside exponent only on the variable when it also affect the coefficient as well.

Answer 2

(4x²)² = (4x²)(4x²) = 16x⁴ it looks like you only applied the outer exponent to x but not to 4.

 

When you applied the outer exponent of 3 to 2x³ again you applied the power-to-a-power to the x part but not the 2.   (2x³)³ = (2x³)(2x³)(2x³)