Which expression is equivalent to (7x^3)^2(x^8)^1/2

Question

(A) 14x^10

(B) 49x^10

(C) 14x^7

(D) 49x^7

Answer 1

(7x³)² (x⁸)^1/2

Apply "distributive property of exponents:

7² (x³)² (x⁸)^1/2

Apply "power of a power" rule: (a^m)ⁿ = a^m*n

7² x^3*2 x^8*1/2

49 x⁶ x⁴

Apply "power of products" rule: a^m aⁿ = a^m+n

49 x¹⁰

The equivalent expression is 49x^10

Answer 2

(7x³)²(x⁸)^1/2 can be rewritten as

(7x³)(7x³)(x⁸)^1/2 when you multiply you add the exponents, so 7x³(7x³) = 49x⁽³⁺³⁾=49x⁶

Power to a power, multiply the powers so (x⁸)^1/2 =x^(8×(1/2))=x⁴

multiply it all together you get (49x⁶)(x⁴)=49x⁽⁶⁺⁴⁾=49x¹⁰ (B)