Question

Which expressions are equivalent to (x⁷)? There may be more than one correct answer. Select all that apply.

a. (x²¹/13)

b. (x¹⁵ ⋅ x⁸)

c. (x²¹ ⋅ x¹³)

d. (x³/x⁴)

Answer 1

The expressions equivalent to (x⁷) are evaluated using exponent rules. Only option b, (x¹⁵ ⋅ x⁸), which simplifies to x¹⁹, is equivalent to (x⁷). No other options provided equate to (x⁷) when simplified correctly.

Step-by-step explanation:

The question pertains to identifying which expressions are equivalent to (x⁷), which involves understanding the rules of exponents. These rules can be applied to multiplication, division, and powers of expressions with exponents.

• a. (x²¹/13) simplifies to (x²)^(21/13) which is not equivalent to (x⁷).
• b. (x¹⁵ ⋅ x⁸) simplifies to x^(15+8) which is x¹¹ and this is equivalent to (x⁷).
• c. (x²¹ ⋅ x¹¹) simplifies to x^(21+13) which is x¹⁴ and not equivalent to (x⁷).
• d. (x³/x⁴) simplifies to x^(3-4) which is x⁻¹ and it is not equivalent to (x⁷).

From these evaluations, we can see that only option b is equivalent to (x⁷), since when you multiply exponents with the same base, you add the exponents together.