Question

Which expressions are equivalent? Justify your reasoning.

fourth root of x cubed
one over x to the negative one power
tenth root of the quantity x to the fifth times x to the fourth times x squared end quantity
x to the one third power times x to the one third power times x to the one third power

Answer 1

The expression with a single rational exponent as follows

What is exponents and powers?

Exponents are often known as powers or indices. In simple terms, power can be defined as an expression that represents repeated multiplication of the same number whereas exponent is the quantity that represents the power to which the number is raised.

1) The expression ⁴√x³ can be expressed as;

x^{\frac{3}{4} }x

4

3

2)The expression ¹/x⁻¹.

This is expressed as a single rational exponent as x

3) The given expression as a single rational exponent.

The expression is; ¹⁰√(x⁵ · x⁴ · x²)

¹⁰√(x¹¹) = x^{(11/10)}x

(11/10)

4) x^{(1/3)} * x^{(1/3)} * x^{(1/3)}x

(1/3)

∗x

(1/3)

∗x

(1/3)

x¹ = x