Chapter 0, Problem 3T

(a)

To determine

To calculate: The value of the question mark in the expression $x^4\cdot x^4=x^{?}$.

(b)

To determine

To calculate: The value of the question mark in the expression $x^0=?,\text{if}x\ne 0$.

(c)

To determine

To calculate: The value of the question mark in the expression $\sqrt{x}=x^{?}$ without using a calculator.

(d)

To determine

To calculate: The value of the question mark in the expression ${\left(x^{-5}\right)}^2=x^{?}$.

(e)

To determine

To calculate: The value of the question mark in the expression $a^{27}÷a^{-3}=a^{?}$.

(f)

To determine

To calculate: The value of the question mark in the expression $x^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\cdot x^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=x^{?}$.

(g)

To determine

To calculate: The value of the question mark in the expression $\frac{1}{\sqrt[3]{x^2}}=\frac{1}{x^{?}}$.

(h)

To determine

To calculate: The value of the question mark in the expression $\frac{1}{x^3}=x^{?}$.