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Chapter 5: Q43. (page 227)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Write down the given information.

The given expression is $y^{28} = y^{3 r} 鈰� y^{7}$ .

02

Step 2. Calculation.

Simplifying the given expression $y^{28} = y^{3 r} 鈰� y^{7}$ .

$\begin{matrix} y^{28} = y^{3 r} 鈰� y^{7} .... (Given) \\ y^{28} = y^{3 r + 7} \\ 28 = 3 r + 7.... (\begin{array}{l} If x^{a} = x^{b} \\ then a = b \end{array}) \\ 3 r = 28 鈭� 7 \\ 3 r = 21 \\ r = 7 \end{matrix}$

03

Step 3. Conclusion.

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

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