Question

1. simplify: ( x^{\frac{3}{4}} \times x^{\frac{1}{4}} )

a. ( x^2 )
b. ( x^{\frac{3}{16}} )
c. ( x^{\frac{1}{2}} )
d. ( x^1 )

Explanation:

Step1: Recall exponent rule

When multiplying exponents with the same base, we use the rule \(a^m\times a^n=a^{m + n}\). Here, the base is \(x\), \(m=\frac{3}{4}\) and \(n=\frac{1}{4}\).

Step2: Add the exponents

\(\frac{3}{4}+\frac{1}{4}=\frac{3 + 1}{4}=\frac{4}{4}=1\). So \(x^{\frac{3}{4}}\times x^{\frac{1}{4}}=x^{1}\).

Answer:

d. \(x^{1}\)