b) $$ \frac{\left(y^{3}\right)^{6}}{y^{15}} $$

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UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{\left(y^{3}\right)^{6}}{y^{15}}
$$

follow these steps using the laws of exponents:

### Step 1: Apply the Power of a Power Rule

The **Power of a Power** rule states that $$(a^{m})^{n} = a^{m \times n}$$. Apply this to $$\left(y^{3}\right)^{6}$$:

$$
\left(y^{3}\right)^{6} = y^{3 \times 6} = y^{18}
$$

### Step 2: Rewrite the Expression

Substitute $$y^{18}$$ back into the original expression:

$$
\frac{y^{18}}{y^{15}}
$$

### Step 3: Apply the Quotient Rule

The **Quotient** rule for exponents states that $$\frac{a^{m}}{a^{n}} = a^{m - n}$$. Apply this to $$\frac{y^{18}}{y^{15}}$$:

$$
\frac{y^{18}}{y^{15}} = y^{18 - 15} = y^{3}
$$

### Final Simplified Form

$$
y^{3}
$$

**Therefore, the simplified form of $$\frac{\left(y^{3}\right)^{6}}{y^{15}}$$ is $$y^{3}$$.**
The simplified form of $$\frac{\left(y^{3}\right)^{6}}{y^{15}}$$ is $$y^{3}$$.

b)

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