All 303 families

GB-13-03-001 · Power of a product

Simplify (4x21y14)2(4x^{21}y^{14})^2.

Index Laws: Power of a Product Booklet p. 1
Method
Use (xᵃ)ᵇ = xᵃᵇ: raise the numerical coefficient to the power, and multiply each variable's power by the outside power
Worked Example (GB-13-03-001)
Booklet p. 1: (xa)b=xab\mathbf{(x^a)^b = x^{ab}} — Work out numbers, xx, and yy on separate lines!
Numbers: 42=16\text{Numbers: } 4^{2} = \mathbf{16}
x term: (x21)2=x21×2=x42x\text{ term: } (x^{21})^{2} = x^{21 \times 2} = \mathbf{x^{42}}
y term: (y14)2=y14×2=y28y\text{ term: } (y^{14})^{2} = y^{14 \times 2} = \mathbf{y^{28}}
16x42y2816x^{42}y^{28}