(why to the power five over Y to the power of three) to the power of three times (why to the eighth power over why to the six power) to the power four fully simplify

Answer 1

To simplify the expression \(\left(\frac{y^5}{y^3}\right)^3 \times \left(\frac{y^8}{y^6}\right)^4\), we can follow these steps:

1. Simplify each term inside the parentheses before applying the powers.

   a. For \(\frac{y^5}{y^3}\): \[ \frac{y^5}{y^3} = y^{5-3} = y^2 \]

   b. For \(\frac{y^8}{y^6}\): \[ \frac{y^8}{y^6} = y^{8-6} = y^2 \]

2. Now substitute these simplified terms back into the expression: \[ \left(y^2\right)^3 \times \left(y^2\right)^4 \]

3. Now apply the power to each term: a. For \(\left(y^2\right)^3\): \[ \left(y^2\right)^3 = y^{2 \cdot 3} = y^6 \]

   b. For \(\left(y^2\right)^4\): \[ \left(y^2\right)^4 = y^{2 \cdot 4} = y^8 \]

4. Now multiply the two results together: \[ y^6 \times y^8 = y^{6+8} = y^{14} \]

Thus, the fully simplified expression is: \[ \boxed{y^{14}} \]