Question

(2qp^3)^3
Select one:
a.
8q^3p^9
b.
−8p^3q^9
c.
m^3p^12p^6
d.
27q^3p^9

Answer 1

The rule of raising a product to an exponent:
Raise every factor to the exponent.

Rule:
\((abc)^n = a^nb^nc^n\)

The rule of raising an exponent to an exponent:
Multiply the exponents.

Rule: \((a^m)^n = a^{m \times n} = a ^{mn}\)

Example using both rules above:
\((3x^2y^5z)^3 = 3^3 (x^2)^3(y^5)^3(z^1)^3 = 27x^{2 \times 3}y^{5 \times 3}z^{1 \times 3} = 27x^6y^{15}z^3\)