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Question

1.b^2(a^3b)^2 +a^2(a^2b^2)^2
2.(-2x^2y^3)^4(xy)^3
3.(a^n+1b^m+2)^3 n+1,m+2 are both powers
4.(c^3d)^a(cd^7)^a

Answer 1

Fror these, remember that (1) a power raised to a power means you multiply the two together, and (2) add the exponents of bases that are multiplied. So,

1. b^2(a^3b)^2 + a^2(a^2b^2)^2 = b^2(a^6b) + a^2(a^4b^4)
= (a^6b)(b^2) + (a^6b)(a^2)(b^4)
= (a^6b)(b^2)(1 + a^2b^2)

2. (-2x^2y^3)^4(xy)^3 = (-2x^8)(y^12)(x^3)(y^3)
= (-2x^11)(y^15)

3. (a^(n+1)b^(m+2))^3 = (a^3(n+1))(b^3(m+2))

4. (c^3d)^a(cd^7)^a = (c^3a)(d^a)(c^a)(d^7a)
= (c^4a)(d^8a)