Question

Enter an expression equivalent to x⁴ × x⁻⁶, in the form xᶜ.

Answer 1

To simplify the expression x⁴ × x⁻⁶, we can add the exponents since the bases are the same. So, x⁴ × x⁻⁶ is equivalent to x⁻².

Step-by-step explanation:

To simplify the expression x⁴ × x⁻⁶, we can add the exponents since the bases are the same. The rule for multiplying exponents with the same base is to add the exponents. So, x⁴ × x⁻⁶ can be written as x^(4 + -6), which simplifies to x^-2.

Another way to think about it is that x⁻⁶ is the reciprocal of x⁶ (since a negative exponent represents the reciprocal of the positive exponent). So, x⁴ × x⁻⁶ is the same as x⁴ × (1/x⁶), which simplifies to 1/x² or x⁻².

Therefore, the expression x⁴ × x⁻⁶ is equivalent to x⁻².