Multiply x to the 1 third power times x to the 3 seventh power.

Solution:

x to the 1 third power times x to the 3 sevenths power

⇒ x^1/3 × x^3/7

By Law of indices or the law of exponents, to multiply two exponents with the same base, we need to add its powers and raise them to that base. 3² × 3⁴  =  (3×3) × (3× 3×3 × 3)= 3⁶

a^p.a^q = a^p+q

∴ x^1/3 ×  x^3/7 = x^{(1/3 + 3/7)} = x^10/21

Multiply x to the 1 third power times x to the 3 seventh power.

Summary:

Multiplying x to the 1 third power times x to the 3 seventh power we get, x^10/21.