Simplify the following. a) ((y^-3 x y2) / y^-7)1/2

July 2, 2026Mathematics

ScanSolve AI Answer

July 2, 2026

Answer

$y^3$

Step 1: Simplify the numerator using the rule $a^m \times a^n = a^{m+n}$ . $y^{-3} \times y^2 = y^{-3+2} = y^{-1}$

Step 2: Simplify the fraction using the rule $\frac{a^m}{a^n} = a^{m-n}$ . $\frac{y^{-1}}{y^{-7}} = y^{-1 - (-7)} = y^{-1+7} = y^6$

Step 3: Apply the outer exponent using the rule $(a^m)^n = a^{m \times n}$ . $(y^6)^{\frac{1}{2}} = y^{6 \times \frac{1}{2}} = y^3$

The simplified expression is: $\boxed{y^3}$ Send me the next one 📸

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Simplify the numerator using the rule a^m × a^n = a^m+n. y^-3 × y^2 = y^-3+2 = y^-1 Step 2: Simplify the fraction using the rule (a^m)/(a^n) = a^m-n.

Asked on July 2, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on July 2, 2026

Step 1: Simplify the numerator using the rule a^m × a^n = a^m+n. y^-3 × y^2 = y^-3+2 = y^-1 Step 2: Simplify the fraction using the rule (a^m)/(a^n) = a^m-n. y^-1y^-7 = y^-1 - (-7) = y^-1+7 = y^6 Step 3: Apply the outer exponent using the rule (a^m)^n = a^m × n. (y^6)^(1)/(2) = y^6 × (1)/(2) = y^3 The simplified expression is: y^3 Send me the next one 📸