Question

What value of r makes$y^{28}=y^{3r}\cdot y^7$ true?

Short answer

The value of$r=7$makes the given expressiontrue.

Step-by-step solution

Step 1. Write down the given information.

The given expression is $y^{28}=y^{3r}\cdot y^7$.

Step 2. Calculation.

Simplifying the given expression $y^{28}=y^{3r}\cdot y^7$.

$\begin{array}{c}{y}^{28}=y^{3r}\cdot y^7\mathrm{....}\left(\text{Given}\right)\\ y^{28}=y^{3r+7}\\ 28=3r+\mathrm{7....}\left(\begin{array}{l}\text{If}{x}^a=x^b\\ \text{then}a=b\end{array}\right)\\ 3r=28-7\\ 3r=21\\ r=7\end{array}$

Step 3. Conclusion.

The value of $r=7$ makes the given expression true.