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

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1. mathstudent55

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: $$(3x^2y^5z)^3 = 3^3 (x^2)^3(y^5)^3(z^1)^3 = 27x^{2 \times 3}y^{5 \times 3}z^{1 \times 3} = 27x^6y^{15}z^3$$