Question

Product rule with negative... Simplify. 3v ⁻² x 5x ⁸ + V ⁹ + ux² x 5u⁻¹

Use only positive exponents in your answer.

Answer 1

To simplify the expression with negative exponents, we apply the product rule for exponents and rewrite any terms with negative exponents with positive ones by placing them in the denominator; the final simplified terms with only positive exponents are 15x⁸/v² for the first term, V⁹ remains unchanged, and 5x²u for the last term.

Step-by-step explanation:

To simplify the expression 3v ⁻² x 5x ⁸ + V ⁹ + ux² x 5u⁻¹, we need to apply the product rule for exponents and ensure that all exponents in the final answer are positive.

For the term 3v⁻² x 5x⁸, we first simplify by multiplying the coefficients (3 and 5) to get 15. Then, we isolate the variables v and x, so the term becomes 15/v² x⁸. To remove the negative exponent, we rewrite v⁻² as 1/v², so the term is now 15x⁸/v².

The second term, V⁹, remains unchanged as there are no negative exponents.

For the term ux² x 5u⁻¹, we again multiply the coefficients (1and 5) to get 5, and we address the exponents. According to the properties of exponents, when multiplying with the same base, we add the exponents. Since u² x u⁻¹ simplifies to u²¹, which is u¹ or simply u, the terms can be rewritten as 5x²u.

Now, the entire expression is simplified and only includes positive exponents:

• 15x⁸/v²
• V⁹
• 5x²u